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Initial value problems, math, Mathematics
Write a Matlab function MyIVP that solves an initialvalue problem (IVP) for a system of ordinary
differential equations (ODEs) of the form
x ?(t) = f (t, x(t)),
where f : R × Rn ? Rn is an arbitrary function with one onedimensional input (for time t) and one ndimensional input x, and ndimensional output. The function should implement a RungeKutta formula (for example, the rk34 formula or the Dormand & Prince formula).
The initial value x0 is provided by the user of MyIVP. The first line of MyIVP (saved in a file MyIVP.m) should look like this
function [xend,t,xt]=MyIVP(f,x0,tspan,N) Inputs
• f: function defining the righthand side of the ODE. f should accept two arguments: t (a number) and x (an ndimensional vector). The function f should return an ndimensional vector y (the time derivative). Typical calling sequence: y=f(t,x), returning the value of f at time t in position x.
• x0: initial value where integration starts from (ndimensional vector).
• tspan: Starting time and end time for integration. Integration has to run from time t =tspan(1)
to time t =tspan(2).
• N: number of steps for integration. The integration stepsize h=(tspan(2)tspan(1))/N should
be small.
Outputs
• xend: result of integration at t =tspan(2).
• t: vector of times at which intermediate values have been computed (this should have N + 1
entries).
• xt: intermediate values (n × (N + 1)array). xt(:,k) should be the solution at t(k).
You can check the builtin variable nargout inside your function to see if the user wants to get three outputs or only the end value xend. If nargout==1 you don’t need to store the intermediate values.
Posted Date: 3/12/2012 10:19:33 AM  Location : United States
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