Higher order differential equations, Programming Languages

Assignment Help:

We'll start this section off with the material which most text books that will cover in this section. We will take the matter from the Second Order chapter and expand this out to nth order linear differential equations. As we will see almost all of the 2nd order material will very naturally extend out to nth order along with only some bit of new material.

Therefore, let's start things off this time with several fundamental concepts for nth order linear differential equations. The most general nth order linear differential equation is as,

Pn(t) y(n) + Pn-1(t) y(n-1) + ......+ P1(t) y' + P0(t) y = G(t)                            (4)

So we hopefully recall this,

y(m) = dmy/dxm

Several of the theorems and concepts for this material need that y(n)has a coefficient of 1 and therefore if we divide out by Pn (t) we find,

y(n) + pn-1(t) y(n-1) + ......+ p1(t) y' + p0(t) y = g(t)                                    (5)

As we may suspect an initial value problem for an nth order differential equation will need the subsequent n initial conditions.

y(t0) = y?0,       y'(t0) = y?1,      ........                 y(n-1) (t0) = y? (n-1) =  y?(n-1),        (6)


Related Discussions:- Higher order differential equations

Define a prolog predicate that asserts list, Define a Prolog predicate flat...

Define a Prolog predicate flatten(List, FlattenedList)  that asserts List  is any nested list of atoms and  FlattenedList  is the same list with the nesting removed. The atom [] sh

Random number generator guessing game, The GuessingGame class contains a sk...

The GuessingGame class contains a skeleton for a program to play a guessing game with the user. The program should randomly generate an integer between 1 and 10 and then ask the us

Programs to solve the nonlinear algebraic equations, Introduction Each...

Introduction Each module of the course includes a programming project. However, for Modules 5 and 6 we will do a single project to cover both. The purpose of the programming p

What is dynamic binding, Dynamic Binding: - Binding refers to the linking ...

Dynamic Binding: - Binding refers to the linking of a procedure call to the code to be executed in response to the call. Dynamic binding (late binding) means that the code associa

Dating game program, You are to write a program that determines the day of ...

You are to write a program that determines the day of the week for New Year's Day in the year 3000. To do this, you must create your own date class (MyDate) and use the following i

Mobile application in android platform phones, Recent problems in finishing...

Recent problems in finishing implementation: This mobile application is built with Sencha Touch framework. Source code is attached in this zip package. The daily rest calc

Real distinct eigenvalues, Real Distinct Eigenvalues Under this case w...

Real Distinct Eigenvalues Under this case we'll have the real, distinct eigenvalues l 1 ≠l 2 ≠l 3 a and their related eigenvectors, ?h 1 , ?h 2 and  ?h 3   are guarantee

Program converts character array to signed decimal integer, 1. Write a func...

1. Write a function that converts a character array to a signed decimal integer. Function prototype must be as follows: int asciiToInt( char *str, unsigned char* eflag) YOU MAY NO

Create an application to run in the amazon ec2 service, In this assignment ...

In this assignment you will create an application to run in the Amazon EC2 service and you will also create a client that can run on local machine and access your application. You

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