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

The rank correlation coefficient (r), The Rank Correlation Coefficient (R) ...

The Rank Correlation Coefficient (R) Also identified as the spearman rank correlation coefficient, its reasons is to establish whether there is any form of association among tw

Finding absolute extrema, Finding Absolute Extrema : Now it's time to see ...

Finding Absolute Extrema : Now it's time to see our first major application of derivatives.  Specified a continuous function, f(x), on an interval [a,b] we desire to find out the

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

Estimate what is the thickness of the paper, Kenny used a micrometer to mea...

Kenny used a micrometer to measure the thickness of a piece of construction paper. The paper measured halfway among 0.24 millimeters and 0.25 millimeters. What is the thickness of

Prove that if x is a real number then [2x] = [x] + [x + ½ ], Prove that if...

Prove that if x is a real number then [2x] = [x] + [x + ½ ] Ans: Let us consider x be any real number. It comprises two parts: integer and fraction. With no loss of

Complex numbers, Complex Numbers In the radicals section we noted that...

Complex Numbers In the radicals section we noted that we won't get a real number out of a square root of a negative number.  For example √-9 isn't a real number as there is no

One-sided limits, One-sided limits: We do this along with one-sided limits...

One-sided limits: We do this along with one-sided limits.  As the name implies, with one-sided limits we will just looking at one side of the point in question.  Following are the

What is inductive reasoning, What is Inductive Reasoning ? Sometimes we...

What is Inductive Reasoning ? Sometimes we draw conclusions based on our observations. If we observe the same results again and again, we conclude that the event always has the

Finite difference method, Two reservoirs of equal cross sectional areas (31...

Two reservoirs of equal cross sectional areas (315 m 2 ) and at equal elevations are connected by a pipe of length 20 m and cross sectional area 3 m 2 . The reservoir on the left (

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