9 years, 7 days

## Differential equation with piecewise...

Maple 2019

For the DE solution below, Maple returns only one option. I can't get the others. Can anyone help?

wW := unapply(piecewise(0 <= x and x < L/2, 0, L/2 <= x and x <= L, w[0]), x):

eq := k*diff(y(x), x\$4) = wW(x):

dsolve({eq, y(0) = 0, y'(0) = 0, y''(L) = 0, y'''(L)=0}, y(x)) assuming 0 < L

y(x) = -L*w[0]*x^3/(6*k) + L^2*w[0]*x^2/(4*k) + w[0]*x^4/(24*k)

Oliveira

## Maple Standard Style...

Maple 2019

Maple always starts a new document with a 2D input style and Times New Roman font. How to change the boot style? (default).
Oliveira

## Elliptical PDEs...

Maple 2019

pde := (diff(u(r, theta), r) + r * diff(u(r, theta), r, r) + diff(u(r, theta), theta, theta) / r ) / r:
iv := u( 1, theta) = 0, u( 3, theta) = theta, u( r, 0) = 10, u( r, Pi/2) = 0:
Maple 2019 returns a symbolic solution for PDE:
pdsolve([pde, iv], u(r, theta));
But for the numeric option, it returns a message saying that Maple is unable to handle elliptical PDEs.
pdsolve(pde, {iv}, numeric, time = t, range = 1 .. 3);

Error, (in pdsolve/numeric) unable to handle elliptic PDEs
I found it strange.

Oliveira.

## Using xx with pdsolve output = listproce...

Maple 2019

pde := diff(u(x, t), x \$ 4) = diff(u(x, t), t \$ 2);

iv:= subs(L = 100, {u(0, t) = 0, u(L, t) = 0, u(x, 0) = sin(x), D[2](u)(x, 0) = 2*x, D[1, 1](u)(0, t) = 0, D[1, 1](u)(L, t) = 0});

de := pdsolve(pde, iv, numeric):

sa1 := de:-value(output = listprocedure);

sa1:=[x=proc() ... end proc,t=proc() ... end proc,u(x,t)=proc() .. end proc]

With the above procedure it works, but in the most compact form below it does not work.

pdsolve(pde, iv, numeric,output = listprocedure):

Error, (in pdsolve/numeric/par_hyp) invalid arguments for theta scheme: [output = listprocedure]

## PDE with pdsolver...

Maple 2019

with(PDEtools);
pde := diff(c(x, t), x, x) - h*diff(c(x, t), x) = diff(c(x, t), t):

iv := c(0, t) = 0, c(a, t) = 0, c(x, 0) = c0:

de := pdsolve([pde, iv], c(x, t), build);

de := ( )

Does anyone know how to solve this PDE?
Thank you,

Oliveira

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