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Consider the different equation \frac {dy}{dt}=t^3,y(0)=0.a) use elder's method with step size...

Question:

Consider the different equation {eq}\frac {dy}{dt}=t^3,y(0)=0. {/eq}

a) use elder's method with step size {eq}\Delta t=0.1 {/eq} to approximate {eq}y(0.4) {/eq}

b) what issue the exact value of {eq}y(0.4) {/eq}

Numerical Solution of Ordinary Differential Equation (ODE)


The question presents a first-order, ordinary differential equation (ODE) with initial condition (IC) that comprises an initial value problem (IVP). Using the numerical Euler's Method we approximate a solution of the IVP at a point in the unknown's domain. The Euler's Method uses a fixed value of the step size {eq}\Delta t. {/eq} Next we use the separation of variables method to find the exact solution of the IVP and compare the exact value to the approximate numerical value from the Euler's Method above. Other concepts used in this question include regular integration from Calculus.


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a) Given the ordinary differential equation (ODE) along with an initial condition (IC) that comprises an initial value problem (IVP) we have

{eq}\l...

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First-Order Linear Differential Equations

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Chapter 16 / Lesson 3
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In this lesson you'll learn how to solve a first-order linear differential equation. We first define what such an equation is, and then we give the algorithm for solving one of that form. Specific examples follow the more general description of the method.


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