#include \"StdAfx.h\" #include \"iostream\" #include \"iomanip\" using namespace
ID: 3569080 • Letter: #
Question
#include "StdAfx.h"
#include "iostream"
#include "iomanip"
using namespace std;
using std::cout;
using std::endl;
using std::cin;
using std::setw;
#define ErrorTolerance 0.0001
#define MaxSteps 40
void Secant(double a, double b);
double rungekutta3(double t);
double f(double t, double x);
double g(double x);
void main()
{
// Initialize guesses 0.7 and 1.0
double g1 = 0.7;
double g2 = 1.0;
Secant(g(g1), g(g2));
//Press key function to terminate the program.
cout << " Press Any Key to Exit..." << endl;
cin.get();
}
double rungekutta3 (double x0)
{
double h = 0.025; // Initialize step size = 0.025.
double x1, x2, x3; // Runge-Kutta orders.
double t0 = 0.0;
//alpha
double a1 = 1.0 / 2.0;
double a2 = 1.0;
//beta
double b10 = 1.0/2.0;
double b20 = -1.0;
double b21 = 2.0;
//weights
double c0 = 1.0 / 6.0;
double c1 = 4.0 / 6.0;
double c2 = 1.0 / 6.0;
// Define y values.
double y[200];
y[0] = 0;
int i = 0;
cout << " h f(t,x) x1 x2 x3 y" << endl;
for (t0 = 0.0; t0 <= 1.0; t0 = t0 + h)
{
i=i+1;
//Calculate to 3rd orders of Runge-Kutta.
x1 = x0 + h * (b10 * f(t0,x0));
x2 = x0 + h * (b20 * f(t0,x0) + b21 * f(t0 + a1 * h, x0));
x3 = x0 + h * (c0 * f(t0,x0) + c1 * f(t0 + a1 * h, x0) + c2 * f(t0 + a2 * h, x0));
//Calculate y.
y[i] = y[i-1] + (1.00/6.00)*(c0*x1 + c1*x2 + c2*x3)*h;
cout << std::setprecision(4) << t0 << " " << std::setprecision(8) << f(t0,x0) << " " << x1 << " " << x2 << " " << x3 << " " << y[i] << " " << endl;
//Set step forward.
x0 = x3;
}
return x3;
}
//Method to return f(t,x) values.
double f(double t, double x)
{
return (x + 0.09*pow(x,2) + cos(10*t));
}
// Method to return the guess values.
double g(double x)
{
return (x + rungekutta3(x) - 3.0);
}
//Secant method.
void Secant(double a, double b)
{
int i;
double fa, fb, d, m;
fa = g(a);
fb = g(b);
//Print out the values of initial guesses and values of the guessed function.
cout << "x(0) = " << std::setprecision(6) << fa << " x(1) = " << std::setprecision(6) << fb << " x(0) + x(1) - 3 = " << std::setprecision(6) << fa + fb << endl;
//Loop runs 40 times.
for (i = 2; i <= MaxSteps; i++)
{
//Calculate d and f(b).
d = (b - a)/(fb - fa);
b = a;
fb = fa;
//Calculate new d.
d = d * fa;
m = 3 - a;
//Function to check if error tolerance is smaller than 10^-4 or 0.001, then print out the value.
if (fabs(d) < ErrorTolerance)
{
cout << "x(0) = " << std::setw(4) << a << " x(1) = " << std::setw(4) << m << " x(0) + x(1) - 3.0 = " << std::setw(4)<< (a + m) - 3.0 << endl;
cout << " Value is found at: " << a << " and satisfied to within a tolerance of " << ErrorTolerance << endl;
return;
}
//Calculate new a and f(a).
a = a - d;
fa = g(a);
//Print out current values.
cout << "x(0) = " << std::setw(4) << a << " x(1) = " << std::setw(4) << b << " x(0) + x(1) - 3 = " << std::setw(4) << 2*(a + b) - 3.0 << endl;
}
}
Explanation / Answer
To convert the program from C to Java the following statements are need to be changed as follows:
Program Code:
//CtoJava.java
class CtoJava
{
//define the static constants
final static double ErrorTolerance=0.0001;
final static int MaxSteps= 40;
//Secant method
static void Secant(double a, double b)
{
int i;
double fa, fb, d, m;
fa = g(a);
fb = g(b);
//the setpercision() is replaced with %.(numberofdecimal points)f
//Print out the values of initial guesses and values of the guessed function.
System.out.printf("x(0) = %.6f x(1) = %.6f x(0) + x(1) - 3 = %.6f ",fa,fb,fa + fb);
//Loop runs 40 times.
for (i = 2; i <= MaxSteps; i++)
{
//Calculate d and f(b).
d = (b - a)/(fb - fa);
b = a;
fb = fa;
//Calculate new d.
d = d * fa;
m = 3 - a;
//Function to check if error tolerance is smaller than 10^-4 or 0.001, then print out the value.
if (Math.abs(d)< ErrorTolerance)
{
//the setw() is replaced with %(spaces)f
System.out.printf("x(0) = %4f x(1) = %4f x(0) + x(1) - 3.0 = %4f ",a,m,(a + m) - 3.0 );
System.out.printf(" Value is found at: %f and satisfied to within a tolerance of %f" ,a,ErrorTolerance );
return;
}
//Calculate new a and f(a).
a = a - d;
fa = g(a);
//Print out current values.
System.out.printf("x(0) = %4f x(1) = %4f x(0) + x(1) - 3 = %4f ",a,b, 2*(a + b) - 3.0);
}
}
//rungekutta3 method
static double rungekutta3(double x0)
{
double h = 0.025; // Initialize step size = 0.025.
double x1, x2, x3=0; // Runge-Kutta orders.
double t0 = 0.0;
//alpha
double a1 = 1.0 / 2.0;
double a2 = 1.0;
//beta
double b10 = 1.0/2.0;
double b20 = -1.0;
double b21 = 2.0;
//weights
double c0 = 1.0 / 6.0;
double c1 = 4.0 / 6.0;
double c2 = 1.0 / 6.0;
// Define y values.
double y[]=new double[200];
y[0] = 0;
int i = 0;
//declare a char of single blank space
char s=' ';
//in the printf statement specify how many spaces are
//required and print the character(eg. %5s=>5 spaces followed by blank space)
//as shown in the below code
System.out.printf(" h %8s f(t,x) %8s x1 %11s x2 %12s x3 %12s y",s,s, s, s, s);
System.out.println();
for (t0 = 0.0; t0 <= 1.0; t0 = t0 + h)
{
i=i+1;
//Calculate to 3rd orders of Runge-Kutta.
x1 = x0 + h * (b10 * f(t0,x0));
x2 = x0 + h * (b20 * f(t0,x0) + b21 * f(t0 + a1 * h, x0));
x3 = x0 + h * (c0 * f(t0,x0) + c1 * f(t0 + a1 * h, x0) + c2 * f(t0 + a2 * h, x0));
//Calculate y.
y[i] = y[i-1] + (1.00/6.00)*(c0*x1 + c1*x2 + c2*x3)*h;
//the setpercision() is replaced with %.(numberofdecimal points)f
System.out.printf("%.4f %.8f %f %f %f %f ",t0, f(t0,x0),x1, x2,x3, y[i]);
//Set step forward.
x0 = x3;
}
return x3;
}
//f method
static double f(double t, double x)
{
return (x + 0.09*Math.pow(x,2) + Math.cos(10*t));
}
//g method
static double g(double x)
{
System.out.println(x + rungekutta3(x) - 3.0);
return x + rungekutta3(x) - 3.0;
}
//main method
public static void main(String args[])
{
// Initialize guesses 0.7 and 1.0
double g1 = 0.7;
double g2 = 1.0;
double gg1=g(g1);
double gg2=g(g2);
Secant(gg1, gg2);
}
}
Sample Output:
h f(t,x) x1 x2 x3 y
0.0000 1.74410000 0.721801 0.743212 0.743343 0.003082
0.0250 1.76198564 0.765368 0.785472 0.786372 0.006341
0.0500 1.71960879 0.807867 0.826031 0.827644 0.009772
0.0750 1.62098233 0.847906 0.863634 0.865860 0.013361
0.1000 1.47363599 0.884280 0.897244 0.899944 0.017092
0.1250 1.28815759 0.916046 0.926109 0.929116 0.020946
0.1500 1.07754650 0.942586 0.949809 0.952936 0.024901
0.1750 0.85641720 0.963641 0.968282 0.971333 0.028934
0.2000 0.64010033 0.979334 0.981830 0.984617 0.033025
0.2250 0.44369569 0.990163 0.991104 0.993454 0.037156
0.2500 0.28113545 0.996968 0.997064 0.998829 0.041312
0.2750 0.16431644 1.000883 1.000919 1.001991 0.045483
0.3000 0.10235693 1.003270 1.004056 1.004368 0.049666
0.3250 0.10102619 1.005631 1.007956 1.007488 0.053864
0.3500 0.16238418 1.009518 1.014100 1.012881 0.058085
0.3750 0.28465535 1.016439 1.023881 1.021987 0.062345
0.4000 0.46234501 1.027767 1.038519 1.036068 0.066663
0.4250 0.68659030 1.044651 1.058986 1.056131 0.071063
0.4500 0.94572265 1.067953 1.085950 1.082868 0.075574
0.4750 1.22600437 1.098193 1.119733 1.116615 0.080222
0.5000 1.51249163 1.135521 1.160294 1.157335 0.085037
0.5250 1.78996816 1.179709 1.207238 1.204621 0.090047
0.5500 2.04389094 1.230170 1.259840 1.257728 0.095274
0.5750 2.26128931 1.285994 1.317093 1.315617 0.100739
0.6000 2.43156310 1.346011 1.377773 1.377025 0.106457
0.6250 2.54713231 1.408864 1.440520 1.440547 0.112437
0.6500 2.60390055 1.473096 1.503923 1.504722 0.118683
0.6750 2.60150574 1.537241 1.566606 1.568129 0.125191
0.7000 2.54334398 1.599921 1.627323 1.629475 0.131954
0.7250 2.43636567 1.659929 1.685031 1.687678 0.138959
0.7500 2.29065590 1.716311 1.738962 1.741938 0.146191
0.7750 2.11882365 1.768423 1.788668 1.791790 0.153632
0.8000 1.93523554 1.815980 1.834060 1.837133 0.161264
0.8250 1.75513977 1.859072 1.875410 1.878243 0.169069
0.8500 1.59373294 1.898165 1.913344 1.915760 0.177032
0.8750 1.46522711 1.934076 1.948801 1.950652 0.185143
0.9000 1.38197512 1.967926 1.982987 1.984156 0.193396
0.9250 1.35371003 2.001078 2.017299 2.017714 0.201790
0.9500 1.38694728 2.035051 2.053245 2.052880 0.210333
0.9750 1.48458902 2.071438 2.092356 2.091234 0.219036
h f(t,x) x1 x2 x3 y
0.0000 2.09000000 1.026125 1.051860 1.051990 0.004365
0.0250 2.12050440 1.078497 1.103083 1.103982 0.008945
0.0500 2.09125493 1.130123 1.152933 1.154546 0.013734
0.0750 2.00620224 1.179623 1.200166 1.202392 0.018722
0.1000 1.87281107 1.225802 1.243756 1.246456 0.023894
0.1250 1.70160679 1.267726 1.282957 1.285964 0.029231
0.1500 1.50553439 1.304783 1.317357 1.320483 0.034713
0.1750 1.29916764 1.336723 1.346898 1.349949 0.040320
0.2000 1.09781528 1.363672 1.371889 1.374676 0.046033
0.2250 0.91657848 1.386133 1.392985 1.395335 0.051834
0.2500 0.76941738 1.404952 1.411152 1.412918 0.057710
0.2750 0.66828544 1.421271 1.427606 1.428678 0.063655
0.3000 0.62238656 1.436458 1.443744 1.444056 0.069666
0.3250 0.63760321 1.452026 1.461058 1.460591 0.075747
0.3500 0.71613309 1.469542 1.481046 1.479827 0.081909
0.3750 0.85635813 1.490532 1.505119 1.503226 0.088169
0.4000 1.05295465 1.516388 1.534523 1.532073 0.094549
0.4250 1.29723716 1.548288 1.570257 1.567402 0.101074
0.4500 1.57771301 1.587123 1.613020 1.609938 0.107775
0.4750 1.88081116 1.633448 1.663173 1.660055 0.114682
0.5000 2.19173770 1.687452 1.720716 1.717756 0.121827
0.5250 2.49540311 1.748948 1.785296 1.782678 0.129238
0.5500 2.77736287 1.817395 1.856234 1.854122 0.136944
0.5750 3.02471330 1.891931 1.932572 1.931096 0.144967
0.6000 3.22688843 1.971432 2.013136 2.012388 0.153326
0.6250 3.37631067 2.054592 2.096613 2.096639 0.162032
0.6500 3.46885761 2.140000 2.181639 2.182439 0.171094
0.6750 3.50411825 2.226240 2.266888 2.268411 0.180512
0.7000 3.48542462 2.311978 2.351157 2.353308 0.190283
0.7250 3.41965757 2.396054 2.433447 2.436093 0.200398
0.7500 3.31683824 2.477554 2.513032 2.516008 0.210847
0.7750 3.18952947 2.555877 2.589506 2.592628 0.221615
0.8000 3.05208222 2.630779 2.662819 2.665892 0.232690
0.8250 2.91977195 2.702389 2.733285 2.736118 0.244059
0.8500 2.80787692 2.771217 2.801572 2.803989 0.255713
0.8750 2.73075510 2.838123 2.868668 2.870518 0.267646
0.9000 2.70097693 2.904281 2.935829 2.936998 0.279858
0.9250 2.72856916 2.971105 3.004513 3.004927 0.292354
0.9500 2.82041820 3.040183 3.076295 3.075930 0.305146
0.9750 2.97987175 3.113179 3.152789 3.151666 0.318254
h f(t,x) x1 x2 x3 y
0.0000 0.79515674 -0.198826 -0.189277 -0.189146 -0.000795
0.0250 0.78298590 -0.179359 -0.171492 -0.170592 -0.001515
0.0500 0.70960935 -0.161722 -0.156183 -0.154570 -0.002168
0.0750 0.57926880 -0.147329 -0.144623 -0.142398 -0.002771
0.1000 0.39972964 -0.137401 -0.137861 -0.135161 -0.003343
0.1250 0.18180597 -0.132888 -0.136654 -0.133647 -0.003908
0.1500 -0.06130266 -0.134414 -0.141426 -0.138299 -0.004490
0.1750 -0.31482397 -0.142235 -0.152234 -0.149183 -0.005115
0.2000 -0.56332647 -0.156224 -0.168772 -0.165985 -0.005808
0.2250 -0.79167860 -0.175881 -0.190382 -0.188032 -0.006590
0.2500 -0.98599387 -0.200357 -0.216100 -0.214335 -0.007478
0.2750 -1.13450254 -0.228516 -0.244716 -0.243644 -0.008485
0.3000 -1.22829373 -0.258998 -0.274845 -0.274533 -0.009619
0.3250 -1.26187945 -0.290306 -0.305018 -0.305486 -0.010880
0.3500 -1.23354327 -0.320905 -0.333772 -0.334991 -0.012263
0.3750 -1.14545019 -0.349309 -0.359744 -0.361637 -0.013756
0.4000 -1.00351023 -0.374181 -0.381752 -0.384202 -0.015343
0.4250 -0.81700476 -0.394415 -0.398874 -0.401729 -0.017004
0.4500 -0.59800034 -0.409204 -0.410503 -0.413586 -0.018716
0.4750 -0.36058877 -0.418093 -0.416386 -0.419504 -0.020454
0.5000 -0.12000294 -0.421004 -0.416637 -0.419596 -0.022195
0.5250 0.10833472 -0.418242 -0.411733 -0.414351 -0.023917
0.5500 0.30977097 -0.410478 -0.402485 -0.404597 -0.025601
0.5750 0.47132839 -0.398705 -0.389981 -0.391457 -0.027233
0.6000 0.58250465 -0.384176 -0.375527 -0.376275 -0.028804
0.6250 0.63591679 -0.368326 -0.360560 -0.360533 -0.030312
0.6500 0.62775276 -0.352687 -0.346562 -0.345762 -0.031760
0.6750 0.55800407 -0.338787 -0.334966 -0.333443 -0.033157
0.7000 0.43046615 -0.328062 -0.327071 -0.324919 -0.034519
0.7250 0.25250658 -0.321763 -0.323959 -0.321313 -0.035865
0.7500 0.03461445 -0.320880 -0.326430 -0.323453 -0.037220
0.7750 -0.21024292 -0.326081 -0.334950 -0.331828 -0.038607
0.8000 -0.46741838 -0.337671 -0.349624 -0.346552 -0.040053
0.8250 -0.72149074 -0.355570 -0.370190 -0.367357 -0.041583
0.8500 -0.95722322 -0.379322 -0.396030 -0.393614 -0.043220
0.8750 -1.16051538 -0.408120 -0.426216 -0.424366 -0.044982
0.9000 -1.31928834 -0.440857 -0.459562 -0.458393 -0.046883
0.9250 -1.42424676 -0.476196 -0.494699 -0.494284 -0.048932
0.9500 -1.46946754 -0.512652 -0.530163 -0.530528 -0.051129
0.9750 -1.45277650 -0.548688 -0.564486 -0.565608 -0.053470
h f(t,x) x1 x2 x3 y
0.0000 2.27103656 1.180054 1.208052 1.208183 0.005014
0.0250 2.30846863 1.237039 1.263974 1.264874 0.010263
0.0500 2.28644789 1.293454 1.318704 1.320317 0.015741
0.0750 2.20889694 1.347928 1.371005 1.373230 0.021439
0.1000 2.08325106 1.399271 1.419855 1.422555 0.027343
0.1250 1.92000743 1.446555 1.464517 1.467524 0.033434
0.1500 1.73208698 1.489175 1.504580 1.507706 0.039695
0.1750 1.53404634 1.526882 1.539993 1.543045 0.046105
0.2000 1.34118680 1.559810 1.571068 1.573856 0.052645
0.2250 1.16861402 1.588463 1.598466 1.600815 0.059300
0.2500 1.03030649 1.613694 1.623155 1.624920 0.066058
0.2750 0.93825094 1.636648 1.646358 1.647430 0.072911
0.3000 0.90169989 1.658701 1.669479 1.669791 0.079860
0.3250 0.92659927 1.681373 1.694018 1.693550 0.086910
0.3500 1.01522362 1.706240 1.721483 1.720264 0.094071
0.3750 1.16604287 1.734840 1.753299 1.751405 0.101362
0.4000 1.37382951 1.768578 1.790724 1.788273 0.108807
0.4250 1.62999888 1.808648 1.834777 1.831921 0.116431
0.4500 1.92315995 1.855961 1.886176 1.883094 0.124267
0.4750 2.23984016 1.911092 1.945305 1.942187 0.132347
0.5000 2.56533720 1.974254 2.012187 2.009228 0.140702
0.5250 2.88464292 2.045286 2.086498 2.083881 0.149366
0.5500 3.18338139 2.123673 2.167587 2.165475 0.158365
0.5750 3.44870293 2.208584 2.254525 2.253049 0.167726
0.6000 3.67008031 2.298925 2.346168 2.345421 0.177469
0.6250 3.83995990 2.393420 2.441237 2.441263 0.187607
0.6500 3.95423002 2.490691 2.538397 2.539197 0.198151
0.6750 4.01248009 2.589353 2.636355 2.637878 0.209105
0.7000 4.01803628 2.688103 2.733939 2.736091 0.220466
0.7250 3.97777233 2.785813 2.830183 2.832829 0.232229
0.7500 3.90170702 2.881600 2.924389 2.927366 0.244386
0.7750 3.80241221 2.974896 3.016185 3.019307 0.256927
0.8000 3.69426630 3.065485 3.105553 3.108626 0.269842
0.8250 3.59259767 3.153533 3.192840 3.195673 0.283120
0.8500 3.51276990 3.239582 3.278749 3.281166 0.296756
0.8750 3.46926463 3.324532 3.364308 3.366158 0.310747
0.9000 3.47481959 3.409593 3.450815 3.451984 0.325098
0.9250 3.53967602 3.496230 3.539776 3.540191 0.339817
0.9500 3.67098422 3.586078 3.632823 3.632458 0.354921
0.9750 3.87240558 3.680863 3.731629 3.730507 0.370433
x(0) = -3.774374 x(1) = 1.882174 x(0) + x(1) - 3 = -1.892200
h f(t,x) x1 x2 x3 y
0.0000 1.74296601 0.720780 0.742177 0.742307 0.003078
0.0250 1.76081165 0.764318 0.784407 0.785307 0.006333
0.0500 1.71839328 0.806787 0.824936 0.826549 0.009758
0.0750 1.61972401 0.846795 0.862507 0.864733 0.013343
0.1000 1.47233378 0.883137 0.896085 0.898785 0.017069
0.1250 1.28681064 0.914870 0.924917 0.927923 0.020918
0.1500 1.07615417 0.941375 0.948581 0.951708 0.024868
0.1750 0.85497898 0.962395 0.967018 0.970070 0.028896
0.2000 0.63861581 0.978052 0.980529 0.983316 0.032982
0.2250 0.44216447 0.988843 0.989765 0.992114 0.037107
0.2500 0.27955704 0.995609 0.995685 0.997451 0.041257
0.2750 0.16269019 0.999484 0.999499 1.000572 0.045422
0.3000 0.10068192 1.001830 1.002595 1.002907 0.049599
0.3250 0.09930114 1.004148 1.006452 1.005984 0.053791
0.3500 0.16060737 1.007991 1.012551 1.011333 0.058006
0.3750 0.28282457 1.014868 1.022286 1.020393 0.062259
0.4000 0.46045752 1.026149 1.036877 1.034427 0.066570
0.4250 0.68464280 1.042985 1.057296 1.054441 0.070963
0.4500 0.94371128 1.066237 1.084210 1.081127 0.075466
0.4750 1.22392480 1.096426 1.117940 1.114822 0.080107
0.5000 1.51033907 1.133702 1.158448 1.155488 0.084915
0.5250 1.78773746 1.177835 1.205336 1.202719 0.089916
0.5500 2.04157668 1.228239 1.257880 1.255768 0.095135
0.5750 2.25888593 1.284004 1.315072 1.313596 0.100592
0.6000 2.42906500 1.343960 1.375690 1.374943 0.106302
0.6250 2.54453397 1.406749 1.438373 1.438400 0.112273
0.6500 2.60119663 1.470915 1.501708 1.502507 0.118509
0.6750 2.59869113 1.534991 1.564321 1.565844 0.125008
0.7000 2.54041389 1.597599 1.624964 1.627116 0.131761
0.7250 2.43331563 1.657532 1.682596 1.685243 0.138756
0.7500 2.28748177 1.713836 1.736447 1.739424 0.145978
0.7750 2.11552154 1.765868 1.786071 1.789193 0.153408
0.8000 1.93180173 1.813340 1.831377 1.834450 0.161028
0.8250 1.75157057 1.856345 1.872638 1.875471 0.168822
0.8500 1.59002454 1.895346 1.910479 1.912896 0.176773
0.8750 1.46137535 1.931163 1.945840 1.947691 0.184872
0.9000 1.37797533 1.964915 1.979926 1.981095 0.193112
0.9250 1.34955672 1.997965 2.014134 2.014549 0.201493
0.9500 1.38263400 2.031832 2.049973 2.049608 0.210022
0.9750 1.48010809 2.068109 2.088972 2.087850 0.218711
x(0) = 0.698993 x(1) = -0.208766 x(0) + x(1) - 3 = -2.019546
h f(t,x) x1 x2 x3 y
0.0000 1.80440209 0.775882 0.798047 0.798177 0.003310
0.0250 1.82442771 0.820983 0.841868 0.842768 0.006804
0.0500 1.78427320 0.865071 0.884043 0.885656 0.010475
0.0750 1.68793980 0.906755 0.923320 0.925546 0.014312
0.1000 1.54294507 0.944832 0.958663 0.961363 0.018299
0.1250 1.35986516 0.978361 0.989321 0.992328 0.022416
0.1500 1.15168918 1.006724 1.014874 1.018001 0.026641
0.1750 0.93302381 1.029663 1.035262 1.038313 0.030953
0.2000 0.71919518 1.047303 1.050787 1.053575 0.035331
0.2250 0.52530271 1.060141 1.062102 1.064451 0.039756
0.2500 0.36528285 1.069017 1.070165 1.071931 0.044216
0.2750 0.25104173 1.075069 1.076188 1.077260 0.048700
0.3000 0.19171195 1.079657 1.081560 1.081871 0.053205
0.3250 0.19308186 1.084285 1.087761 1.087293 0.057735
0.3500 0.25723470 1.090508 1.096276 1.095057 0.062298
0.3750 0.38242150 1.099838 1.108501 1.106608 0.066909
0.4000 0.56317632 1.113647 1.125660 1.123209 0.071589
0.4250 0.79066595 1.133093 1.148729 1.145874 0.076363
0.4500 1.05325093 1.159040 1.178381 1.175299 0.081257
0.4750 1.33722080 1.192014 1.214944 1.211826 0.086301
0.5000 1.62765574 1.232172 1.258385 1.255425 0.091524
0.5250 1.90935910 1.279292 1.308314 1.305697 0.096954
0.5500 2.16780225 1.332794 1.364013 1.361901 0.102614
0.5750 2.39002314 1.391776 1.424484 1.423008 0.108526
0.6000 2.56542417 1.455076 1.488511 1.487763 0.114704
0.6250 2.68642214 1.521343 1.554741 1.554767 0.121159
0.6500 2.74891225 1.589129 1.621768 1.622568 0.127894
0.6750 2.75251979 1.656975 1.688227 1.689750 0.134908
0.7000 2.70062538 1.723508 1.752876 1.755028 0.142193
0.7250 2.60016282 1.787530 1.814679 1.817326 0.149737
0.7500 2.46120137 1.848091 1.872873 1.875850 0.157525
0.7750 2.29633700 1.904554 1.927017 1.930139 0.165541
0.8000 2.11992840 1.956638 1.977027 1.980099 0.173767
0.8250 1.94722289 2.004440 2.023179 2.026012 0.182186
0.8500 1.79342524 2.048430 2.066105 2.068522 0.190784
0.8750 1.67276617 2.089431 2.106751 2.108601 0.199551
0.9000 1.59762893 2.128572 2.146328 2.147497 0.208483
0.9250 1.57778915 2.167220 2.186242 2.186657 0.217579
0.9500 1.61981713 2.206905 2.228010 2.227645 0.226847
0.9750 1.72668134 2.249228 2.273173 2.272051 0.236302
x(0) = 0.753327 x(1) = 0.698993 x(0) + x(1) - 3 = -0.095360
h f(t,x) x1 x2 x3 y
0.0000 1.79784054 0.770019 0.792102 0.792233 0.003285
0.0250 1.81763206 0.814953 0.835753 0.836653 0.006754
0.0500 1.77723436 0.858868 0.877753 0.879366 0.010399
0.0750 1.68064993 0.900374 0.916847 0.919073 0.014209
0.1000 1.53539763 0.938265 0.952001 0.954702 0.018168
0.1250 1.35205487 0.971602 0.982464 0.985471 0.022256
0.1500 1.14361187 0.999766 1.007815 1.010942 0.026452
0.1750 0.92467613 1.022500 1.027994 1.031046 0.030734
0.2000 0.71057426 1.039928 1.043304 1.046092 0.035081
0.2250 0.51640572 1.052547 1.054397 1.056746 0.039474
0.2500 0.35610648 1.061197 1.062230 1.063996 0.043901
0.2750 0.24158163 1.067016 1.068017 1.069089 0.048351
0.3000 0.18196222 1.071364 1.073145 1.073456 0.052821
0.3250 0.18303450 1.075744 1.079095 1.078627 0.057315
0.3500 0.24687917 1.081713 1.087351 1.086132 0.061841
0.3750 0.37174435 1.090779 1.099309 1.097416 0.066414
0.4000 0.55216095 1.104318 1.116192 1.113742 0.071055
0.4250 0.77929252 1.123483 1.138978 1.136122 0.075788
0.4500 1.04149638 1.149141 1.168336 1.165254 0.080640
0.4750 1.32505910 1.181817 1.204595 1.201477 0.085641
0.5000 1.61505818 1.221665 1.247720 1.244761 0.090820
0.5250 1.89629480 1.268464 1.297323 1.294705 0.096204
0.5500 2.15423872 1.321633 1.352683 1.350571 0.101817
0.5750 2.37592688 1.380270 1.412801 1.411325 0.107680
0.6000 2.55076135 1.443210 1.476462 1.475714 0.113808
0.6250 2.67115920 1.509103 1.542310 1.542337 0.120212
0.6500 2.73301646 1.576499 1.608940 1.609740 0.126894
0.6750 2.73595974 1.643939 1.674985 1.676508 0.133852
0.7000 2.68337125 1.710050 1.739203 1.741354 0.141080
0.7250 2.58218652 1.773631 1.800556 1.803203 0.148566
0.7500 2.44247644 1.833734 1.858282 1.861258 0.156293
0.7750 2.27683832 1.889719 1.911939 1.915061 0.164247
0.8000 2.09963161 1.941306 1.961441 1.964513 0.172407
0.8250 1.92610363 1.988590 2.007065 2.009898 0.180759
0.8500 1.77145815 2.032041 2.049442 2.051858 0.189288
0.8750 1.64992375 2.072482 2.089517 2.091367 0.197984
0.9000 1.57388023 2.111041 2.128500 2.129669 0.206841
0.9250 1.55309845 2.149083 2.167797 2.168212 0.215861
0.9500 1.59414256 2.188139 2.208923 2.208558 0.225050
0.9750 1.69997361 2.229808 2.253419 2.252297 0.234422
x(0) = 0.747546 x(1) = 0.753327 x(0) + x(1) - 3 = 0.001746
x(0) = 0.747546 x(1) = 2.252454 x(0) + x(1) - 3.0 = 0.000000
Value is found at: 0.747546 and satisfied to within a tolerance of 0.000100
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