Question

Consider the following problem Solve for y(t) in the ODE below (Van der Pol equation) for t ranging from O to 10 seconds with initial conditions yo) = 5 and y'(0) = 0 and mu = 5. Select the methods below that would be appropriate to use for a solution to this problem. More than one method may be applicable. Select all that apply. ? Shooting method Finite difference method MATLAB m-file euler.m from course notes MATLAB m-file odeRK4sys.m from course notes MATLAB function ode45 Fourth order centered differencing MATLAB integral function

Answer 1

FInd the solution of the given vdp equation using ode45 solver of MATLAB:

%================ Main script ===============

% Calliing ode45 solver
[t,y] = ode45(@vdpeq,[0 10],[5; 0]);

plot(t,y(:,1),'-.',t,y(:,2),'-.')
title('Solution of van-der-Pol Equation using ode45 solver with \mu = 5');
xlabel('Time(t)');
ylabel('y');
legend('y_1','y_2')

%========================================

Note: for implementing ode45 solver, we reformulate the given ODE in two first order ODEs using the following function:

%============== van-der-Pol function ===========

function dydt = vdpeq(t,y)
mu=5;
dydt = [y(2); mu*(1-y(1)^2)*y(2)-y(1)];

%=========================================

Solution plot:

Note: The function name must be same as the name of the file it is contained in.