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Use Euler’s Method with a step size of 0.2 to make a table of approximate values of the solution of initial-value problem Use Euler’s Method & Runge Kutta Method with a step size of 0.2 to make a...

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Use Euler’s Method with a step size of 0.2 to make a table of approximate values of the solution of initial-value problem
  1. Use Euler’s Method & Runge Kutta Method with a step size of 0.2 to make a table of approximate values of the solution of initial-value problem

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Question 4 Use Euler’s Method with a step size of 0.2 to make a table of approximate values of the solution of initial-value problem , over the interval . Use Euler’s Method & Runge Kutta Method with a step size of 0.2 to make a table of approximate values of the solution of initial-value problem , over the interval . Question 5 Determine the order and linearity of the following: Show whether the following PDEs are parabolic, hyperbolic or elliptical. Solve the following wave equation: Given the initial condition , determine the particular solution for the following initial boundary value problem.

Answered Same Day Dec 21, 2021

Solution

Robert answered on Dec 21 2021
133 Votes
d) Given the initial condition , determine the particular solution for the
following initial boundary value problem.
ut = kuxx where u(0, t) = 0, u(L, t) = 0, ut(x, 0) = 2 = f(x)
Let u(x,t) = X(x) T(t) be solution.
ut = kuxx ⇒ X(x)T ′(t) = kX ′′(x)T (t)
Divide by X(x) T(t)
T ′(t
T (t)
=...
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