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user21

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Post Reopened by xzczd♦, C. E.♦, kirma, bbgodfrey, halirutan

occurred Aug 11, 2018 at 16:24

Post Closed as "Not suitable for this site" by corey979, MarcoB, m_goldberg, Feyre, user21

occurred Jan 23, 2017 at 8:46

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edited Jan 23, 2017 at 7:02

xzczd ♦

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Solve 2D inhomogeneous biharmonic equation of fourth order

How to solve a fourth order PDE2D inhomogeneous biharmonic equation with ndsolveNDSolve?

I tried the following code:

P[x_, y_] := x y
eq = Laplacian[Laplacian[w[x, y], {x, y}], {x, y}] == x*y;
bc = {w[0, y] == w[1, y] == w[x, 0] == w[x, 1] == 0, 
Derivative[2, 0][w][0, y] == Derivative[2, 0][w][1, y] == 
Derivative[0, 2][w][x, 0] == Derivative[0, 2][w][x, 1] == 0};
NDSolve[{eq == P[x, y], bc}, w, {x, 0, 1}, {y, 0, 1}]

but it says

NDSolve::femcmsd: The spatial derivative order of the PDE may not exceed two.

How to derive the solution?

Solve 2D equation of fourth order

How to solve a fourth order PDE with ndsolve?

I tried the following code:

P[x_, y_] := x y
eq = Laplacian[Laplacian[w[x, y], {x, y}], {x, y}] == x*y;
bc = {w[0, y] == w[1, y] == w[x, 0] == w[x, 1] == 0, 
Derivative[2, 0][w][0, y] == Derivative[2, 0][w][1, y] == 
Derivative[0, 2][w][x, 0] == Derivative[0, 2][w][x, 1] == 0};
NDSolve[{eq == P[x, y], bc}, w, {x, 0, 1}, {y, 0, 1}]

but it says

NDSolve::femcmsd: The spatial derivative order of the PDE may not exceed two.

How to derive the solution?

2D inhomogeneous biharmonic equation

How to solve a 2D inhomogeneous biharmonic equation with NDSolve?

I tried the following code:

P[x_, y_] := x y
eq = Laplacian[Laplacian[w[x, y], {x, y}], {x, y}] == x*y;
bc = {w[0, y] == w[1, y] == w[x, 0] == w[x, 1] == 0, 
Derivative[2, 0][w][0, y] == Derivative[2, 0][w][1, y] == 
Derivative[0, 2][w][x, 0] == Derivative[0, 2][w][x, 1] == 0};
NDSolve[{eq == P[x, y], bc}, w, {x, 0, 1}, {y, 0, 1}]

but it says

NDSolve::femcmsd: The spatial derivative order of the PDE may not exceed two.

How to derive the solution?

plotting differential-equations numerical-integration

improved formatting

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edited Jan 22, 2017 at 11:02

Mariusz Iwaniuk

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How to solve a fourth order PDE with ndsolve?

I tried the following code:

NDSolve[{P[x_, y_] := x y
eq = Laplacian[Laplacian[w[x, y], {x, y}], {x, y}]==P[x] == x*y;
bc = {w[0, y] == w[1, y] == w[x, 0] == w[x, 1] == 0, 
Derivative[2, 0][w][0, y] == Derivative[2, 0][w][1, y] == 
Derivative[0, 2][w][x, 0] == Derivative[0, 2][w][x, 1] == 0};
NDSolve[{eq == P[x, y], bc}, w, {x, 0, 1}, {y, 0, 1}]

but it says

NDSolve::femcmsd: The spatial derivative order of the PDE may not exceed two.

How to derive the solution?

How to solve a fourth order PDE with ndsolve?

I tried the following code:

NDSolve[{Laplacian[Laplacian[w[x,y],{x,y}],{x,y}]==P[x,y],bc},w,{x,0,1},{y,0,1}]

but it says

NDSolve::femcmsd: The spatial derivative order of the PDE may not exceed two.

How to derive the solution?

How to solve a fourth order PDE with ndsolve?

I tried the following code:

P[x_, y_] := x y
eq = Laplacian[Laplacian[w[x, y], {x, y}], {x, y}] == x*y;
bc = {w[0, y] == w[1, y] == w[x, 0] == w[x, 1] == 0, 
Derivative[2, 0][w][0, y] == Derivative[2, 0][w][1, y] == 
Derivative[0, 2][w][x, 0] == Derivative[0, 2][w][x, 1] == 0};
NDSolve[{eq == P[x, y], bc}, w, {x, 0, 1}, {y, 0, 1}]