*THIS PROBLEM REQUIRES THE MATLAB CODE* This is the code i have so far but it ha

Question

*THIS PROBLEM REQUIRES THE MATLAB CODE*

This is the code i have so far but it has some problems i need help fixing. Thanks

%% part a)
x = -0.7:0.7
f = (1)./(1+2.*x.^2);
% first part for n=10
for j = 1:14
su(j)=0;
for n=1:10
su(j)=su(j)+(-1)^n*2^n*x(j)^(2*n);
end
err(j)=abs(f(j)-su(j));
end
True_Relative_Error1=sum(err)

% second part for n=50
for j=1:14
sum1(j)=0;
for n=1:50
sum1(j)=sum1(j)+(-1)^n*2^n*x(j)^(2*n);
end
err1(j)=abs(f(j)-sum1(j));
end
True_Relative_Error2=sum(err1)
%% part b)
figure;
plot(x,f);
hold on
plot(x,su,'r');
legend('Actual Value','Expansion of n=10')
figure;
plot(x,f);
hold on
plot(x,sum1,'b-');
legend('Actual Value','Expansion of n=50')
title('Problem #1 Graph')

Write a Mat lab script to calculate the following Taylor series expansion: y = 1/(1 + 2x^2) 1/1 + 2x^2 = sigma_n = 0^infinity (-2x^2)^n = sigma_n = 0^infinity (-1)^n 2^n x^2n a) The code shall include the calculation of the true relative error, while the format long will be used for calculating y = 1/(1 + 2 times 0.5^2) by Maltab as the true solution. Compare the solution for n = 10 with the solution of n - 50 by calculating the ratio of the two solutions. b) Plot the function y = 1/(1 + 2x^2) for -0.7

Explanation / Answer

CORRECTED MATLAB CODE

clc;
clear all;
close all;
%% part a)
x = -0.7:0.1:0.7
f = (1)./(1+2.*x.^2);
% first part for n=10
for j = 1:14
su(j)=0;
for n=1:10
su(j)=su(j)+(-1)^n*2^n*x(j)^(2*n);
end
err(j)=abs(f(j)-su(j));
end
su
True_Relative_Error1=sum(err)
% second part for n=50
for j=1:14
sum1(j)=0;
for n=1:50
sum1(j)=sum1(j)+(-1)^n*2^n*x(j)^(2*n);
end
err1(j)=abs(f(j)-sum1(j));
end
True_Relative_Error2=sum(err1)
%% part b)
figure;
plot(f);
hold on
plot(su,'r');
legend('Actual Value','Expansion of n=10')
figure;
plot(f, 'b-');
hold on
plot(sum1,'r');
legend('Actual Value','Expansion of n=50')
title('Problem #1 Graph')

Problems in the previous code

1) Step size of vector x was not defined. => x = -0.7:0.1:0.7

2) The x vector has 15 elements and f, su and sum1 vector has 14 elements in each, hence an error in size was occuring . So just put the f, su and sum1 in plot statement and you will get the output plot.

Related Questions

Navigate

• Browse (All)
• Browse #
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.