Initial value problems, math, Mathematics

Assignment Help:
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.

Related Discussions:- Initial value problems, math

Solve the form x2 + bx - c, Solve the form x 2 + bx - c ? This tutori...

Solve the form x 2 + bx - c ? This tutorial will help you factor quadratics that look something like this: x 2 + 11x - 12 (No lead coefficient; positive middle coeffic

Imaginay Number, how to solve imaginary number such as like (-3v-5)² ?? Can...

how to solve imaginary number such as like (-3v-5)² ?? Can I cancel the radical sign and the power of two ? and square the -3 and times to -5 ? hope you will answer this :) thanks

Numerical methods for ordinary differential equationsordinay, #k1=f(Tn, Xn)...

#k1=f(Tn, Xn), k2=f (Tn + H.Y,Xn + H.Y.k1) Xn+1=Xn + H(a.k1+ b.k2) Find a relation between Y,a and b so that the method is second order consistent.

Solving trig equations with calculators part ii, Solving Trig Equations wit...

Solving Trig Equations with Calculators, Part II : Since this document is also being prepared for viewing on the web we split this section into two parts to keep the size of the

Complex number, a ,b,c are complex numbers such that a/1-b=b/1-c=c-1-a=k.fi...

a ,b,c are complex numbers such that a/1-b=b/1-c=c-1-a=k.find the value of k

What is the sample space for this experiment, A die is thrown repeatedly un...

A die is thrown repeatedly until a six comes up. What is the sample space for this experiment? HINT ;A= {6} B={1,2,3,4,5,} Ans: The sample space is = {A, BA, BBA, BBBA, BBBBA.

Differentiation, how to write assignment of the application of differentiat...

how to write assignment of the application of differentiation in science

Arithmetico geometric progression, find the sum of the following series upt...

find the sum of the following series upto n terms: 1*2+2*4+3*8+4*16+.....

Computation of covariance - grouped data, Grouped Data          ...

Grouped Data          For grouped data of a paired population            where,                      f is the

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd