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Question: How do I discretise the 4th order PDE?

Question:How do I discretise the 4th order PDE?

abdulganiy 145 Maple 2016
homework pde numeric differential-equations
May 27 2020
1

Dear All.

Please kindly help to correct the attached code on discretization of fourth order PDE using method of line.
Thank you and kind regards.

restart

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Discretization of parabolic equation with method of line

diff(u(x, t), t) = -2*(diff(diff(u(x, t), x), x))-(diff(diff(diff(diff(u(x, t), x), x), x), x))-u(x, t)*(diff(u(x, t), x))

u(x, t)

u(x, t)

u(x, 0) = 0.3e-1*sin(x)

8

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Convert the BC to finite difference

(1/2)*(u[m+1](t)-u[m-1](t))/h

(u[m-1](t)-2*u[m](t)+u[m+1](t))/h^2

(u[m-2](t)-4*u[m-1](t)+6*u[m](t)-4*u[m+1](t)+u[m+2](t))/h^4

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Convert the governing equation to finite difference form

Error, invalid input: diff received 2*h, which is not valid for its 2nd argument

Error, invalid input: diff received 2*h, which is not valid for its 2nd argument

Error, invalid input: LinearAlgebra:-GenerateMatrix expects its 1st argument, eqns, to be of type ({list, set})({`=`, algebraic}), but received eqs

A

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