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

Integer exponents, We will begin this chapter by looking at integer exponen...

We will begin this chapter by looking at integer exponents.  Actually, initially we will suppose that the exponents are +ve as well. We will look at zero & negative exponents in a

Find the are length and sketch the level curves, 1) Find the are length of ...

1) Find the are length of r(t) = ( 1/2t^2, 1/3t^3, 1/3t^3) where t is between 1 and 3 (greater than or equal less than or equal) 2) Sketch the level curves of f(x,y) = x^2-2y^2

Initial conditions to find system of equations, Solve the subsequent IVP. ...

Solve the subsequent IVP. y′′ + 11y′ + 24 y = 0 y (0) =0  y′ (0)=-7  Solution The characteristic equation is as r 2 +11r + 24 = 0 ( r + 8) ( r + 3) = 0

Reason why we start division, Reasons why we start division : The reason w...

Reasons why we start division : The reason we start division by considering the digit in the leftmost place is efficiency and ease . For instance, suppose we divide 417 by 3, we

Surface area of prisms , Can you help me find out how to find the surface a...

Can you help me find out how to find the surface area of a prism

Daily revenue for next 30 days, Owner of a computer repair shop has daily r...

Owner of a computer repair shop has daily revenue with mean $7200 and SD $1200 Daily revenue for next 30 days will be monitored. What is probability that daily revenue for those 30

Y=Theea[sin(inTheeta)+cos(inTheeta)], Y=θ[SIN(INθ)+COS(INθ)],THEN FIND dy÷d...

Y=θ[SIN(INθ)+COS(INθ)],THEN FIND dy÷dθ. Solution)  Y=θ[SIN(INθ)+COS(INθ)] applying u.v rule then dy÷dθ={[ SIN(INθ)+COS(INθ) ] dθ÷dθ }+ {θ[ d÷dθ{SIN(INθ)+COS(INθ) ] }    => SI

How much greater is 0.0543 than 0.002, How much greater is 0.0543 than 0.00...

How much greater is 0.0543 than 0.002? To ?nd out how much greater a number is, you required to subtract; 0.0543 - 0.002 = 0.0523. For subtract decimals and line the numbers up

Differential equations, Verify Liouville''s formula for y "-y" - y'' + y = ...

Verify Liouville''s formula for y "-y" - y'' + y = 0 in (0, 1) ?

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