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

Build a fine automaton which accept all words, Build a Fine Automaton which...

Build a Fine Automaton which accept all words which have different first and last letters (that is if the word starts with an "a" to be accepted it should end with "b" and vice ver

Doubles Plus 1 and Doubles Minus 1, Write the doubles fact you used to solv...

Write the doubles fact you used to solve the problem. 7 + 8 = 15

Show that the ratio of the volume of the sphere, A sphere and a cube have e...

A sphere and a cube have equal surface areas. Show that the ratio of the volume of the sphere to that of the cube is √6 : √π. Ans:    S.A. of sphere = S.A of cube    4π r 2

How to convert decimals to percentages, Q. How to Convert Decimals to Perce...

Q. How to Convert Decimals to Percentages? Ans. Remember that when you have a decimal number, the digits to the right of the decimal point have the following meaning:

How much money did carlie have after she had paid her friend, Carlie receiv...

Carlie received x dollars every hour she spent babysitting. She babysat a total of h hours. She then gave half of the money to a friend who had stopped through to help her. How muc

Find the middle term of the arithmetic progressions, Find the middle term o...

Find the middle term of the AP 1, 8, 15....505. A ns:    Middle terms a + (n-1)d = 505 a + (n-1)7 = 505 n - 1 = 504/7 n = 73 ∴ 37th term is middle term a 37

Solving multi step equations, can you help me? cause im in 7th grade advanc...

can you help me? cause im in 7th grade advanced math and tomorrow I have a test tomorrow and I don''t get this

Percentage, there are 300 students in the sixth grade. if 40% of them were ...

there are 300 students in the sixth grade. if 40% of them were girls, how many boys were there?

Sum, As1212uestion #Minimum 100 words accepted#

As1212uestion #Minimum 100 words accepted#

6thgrade, do you have 3 digit and 4 digit number problem

do you have 3 digit and 4 digit number problem

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