Write a Matlab function MyIVP that solves an initial-value 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 one-dimensional input (for time t) and one n-dimensional input x, and n-dimensional output. The function should implement a Runge-Kutta 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 right-hand side of the ODE. f should accept two arguments: t (a number) and x (an n-dimensional vector). The function f should return an n-dimensional 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 (n-dimensional 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 built-in 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

Ask an Expert

Related Discussions:- Initial value problems, math, Assignment Help, Ask Question on Initial value problems, math, Get Answer, Expert's Help, Initial value problems, math Discussions

Write discussion on Initial value problems, math
Your posts are moderated

Write your message here..

Related Questions

Fraction, 4/(x+7)(x+4) 4/(x+7)(x+4)

Problem of purchasing, story of faicing problem when customer purchasing a ... story of faicing problem when customer purchasing a product

Geometry, can i get some triangle congruence proofs help? can i get some triangle congruence proofs help?

Probability exercise, 1. A psychologist developed a test designed to help p... 1. A psychologist developed a test designed to help predict whether production-line workers in a large industry will perform satisfactorily. A test was administered to all new empl

Find the circumference of a circle, Find the circumference of a circle whos... Find the circumference of a circle whose area is 16 times the area of the circle with diameter 7cm            (Ans: 88cm) Ans:     Π R 2 = 16 Π  r 2 R 2 = 16 r 2

Precalc, WHAT IS PRECALC WHAT IS PRECALC

Precalculus, A=30, B=45, b=4 A=30, B=45, b=4

Function notation, Function notation: Next we have to take a rapid look at... Function notation: Next we have to take a rapid look at function notation. Function notation is nothing more than way of writing the y in a function which will let to simplify not

Maxima and minima, Maxima and Minima We have to make a distinctio... Maxima and Minima We have to make a distinction between relative maxima (or minima) and global maxima (or minima). Let f(x) be a function of x. Then the global maxi

Metric measurement, what is a liter what is a liter