a) In solving an IVP for an ODE numerically, the global error grows only if the
ID: 3110914 • Letter: A
Question
a) In solving an IVP for an ODE numerically, the global error grows only if the solution sought is unstable. True or False? b) In solving an IVP for an ODE numerically, the global error is always at least as large as the sum of the local truncation errors. True or false? c) What is the basic difference between an explicit method and an implicit method in solving an ODE numerically? d) Describe in words the difference between the local truncation error and the global error in solving an ODE numerically? e) Describe in words the distinction between a stable and an unstable solution of an ODE. f) The stability or instability of an ODE solution can change with time. True or false? g) It is possible for a numerical solution method to be unstable when applied to a stable ODE. True or false? h) For the backward Euler method, which factor places a stronger restriction on the choice of the step size: stability or accuracy? i) What is meant by a stiff ODE and why is it difficult to solve numerically? j) What is the principle drawback of Taylor series methods compared with Runge-Kutta methods for solving ODEs numerically?Explanation / Answer
a)True
b)False
c)Explicit and implicit methods are used to the solutions of tie dependent ordinary and partial differential equations.
explicitt method calculates the state of a system at a later time to the state of a system of a current time.and implicit methods by solving an equation involving both the current state of the system and the later on.
d)the error caused by one iteration is called local truncation errors and the cummulative errors are caused by many iterations is called global truncation errors
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