# Question: a rewrite the differential equation you have been given at...

###### Question details

a) Rewrite the differential equation you have been given at the end of this document in the correct form for applying the Euler and EulerCauchy numerical schemes. Write down an appropriate Euler method recursive scheme to solve this differential equation for the given values of the parameters and the given initial conditions.

b) For this recursive scheme, draw out as much information as you can on the stability of the scheme from its defining equations, including any restrictions on the values of n for which the scheme is stable.

c) Write a C program to implement the Euler Scheme. You may also do this in a spreadsheet if you are not familiar with programming.

d) Using the result of step (c), calculate values of x for the range t = 0 to t = 25.0, using a step size of h = 0.05. Repeat this for the step size h = 0.025.

e) Rewrite your recursive scheme as an Euler-Cauchy scheme for this differential equation. Repeat steps (b) to (d) using this scheme.

f) For each of the two versions of the numerical scheme with both step sizes, compare the value found for xn to the correct value x(tn) on the interval 0 to 30.0. Comment on your result.