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

Find inverse laplace transform, Question: Find Inverse Laplace Transfor...

Question: Find Inverse Laplace Transform of the following (a) F(s) = (s-1)/(2s 2 +8s+13)     (b) F(s)= e -4s /(s 2 +1) + (1/s 3 )

Find the value of the first instalment, A man arranges to pay a debt of Rs....

A man arranges to pay a debt of Rs.3600 in 40 monthly instalments which are in a AP. When 30 instalments are paid he dies leaving one third of the debt unpaid. Find the value of th

Multiply 3 (x + 4) = 3x + 12 to find out the total perimeter, Jake required...

Jake required to find out the perimeter of an equilateral triangle whose sides measure x + 4 cm each. Jake realized that he could multiply 3 (x + 4) = 3x + 12 to find out the total

Division problem, Raul has 56 bouncy balls. He puts three times as many bal...

Raul has 56 bouncy balls. He puts three times as many balls into red gift bags as he puts into green gift bags. If he puts the same number of balls in each bag, how many balls does

Probability of chosen number from 1st 500 divisble by 3or5 , IN THIS WE HAV...

IN THIS WE HAVE TO ADD THE PROBABILITY of 3 and 5  occuring separtely and subtract prob. of 3 and 5 occuring together therefore p=(166+100-33)/500=233/500=0.466

Mechnics, i have many trouble in this subject

i have many trouble in this subject

Permutation, A telephone dialled is numbered 0to9. if 0is dialled first the...

A telephone dialled is numbered 0to9. if 0is dialled first the caller is connected to the international exchange system.find the number of local calls that can be rung if a local n

Demerits and merit-the mode, The mode Merits i.  This can be dete...

The mode Merits i.  This can be determined from incomplete data given the observations along with the highest frequency are already known ii.  The mode has some applic

Rejection and acceptance regions, Rejection and Acceptance regions All ...

Rejection and Acceptance regions All possible values which a test statistic may either suppose consistency along with the null hypothesis as acceptance region or lead to the re

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