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xzczd ♦
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2D Differentiationdifferentiation matrix

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xzczd ♦
xzczd ♦
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DifferentiationMatrix 2D Differentiation matrix

NDSolve``FiniteDifferenceDerivativeNDSolve`FiniteDifferenceDerivative is a very helpful function to calculate numerical derivatives. It is explained in the tutorial The Numerical Method of Lines in more detail.

Here I found the reference BENGT FORNBERG:CALCULATION OF WEIGHTS IN FINITE DIFFERENCE FORMULAS which explains how the weigthsweights are to be calculated in the one dimensional case  .

I couldn't find a similar reference for the twodimensionaltwo dimensional case.

My question:

  • How is the differentiationMatrixdifferentiation matrix evaluated in this case, especially at boundaryboundary meshpoints?
  • Are there additional helpful references in the Mathematica documentation?

Thanks!

DifferentiationMatrix 2D

NDSolve``FiniteDifferenceDerivative is a very helpful function to calculate numerical derivatives. It is explained in the tutorial The Numerical Method of Lines in more detail.

Here I found the reference BENGT FORNBERG:CALCULATION OF WEIGHTS IN FINITE DIFFERENCE FORMULAS which explains how the weigths are to be calculated in the one dimensional case  .

I couldn't find a similar reference for the twodimensional case.

My question:

  • How is the differentiationMatrix evaluated in this case, especially at boundary meshpoints?
  • Are there additional helpful references in the Mathematica documentation?

Thanks!

2D Differentiation matrix

NDSolve`FiniteDifferenceDerivative is a very helpful function to calculate numerical derivatives. It is explained in the tutorial The Numerical Method of Lines in more detail.

Here I found the reference BENGT FORNBERG:CALCULATION OF WEIGHTS IN FINITE DIFFERENCE FORMULAS which explains how the weights are to be calculated in the one dimensional case.

I couldn't find a similar reference for the two dimensional case.

My question:

  • How is the differentiation matrix evaluated in this case, especially at boundary meshpoints?
  • Are there additional helpful references in the Mathematica documentation?

Thanks!

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Ulrich Neumann
Ulrich Neumann
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DifferentiationMatrix 2D

NDSolve``FiniteDifferenceDerivative is a very helpful function to calculate numerical derivatives. It is explained in the tutorial The Numerical Method of Lines in more detail.

Here I found the reference BENGT FORNBERG:CALCULATION OF WEIGHTS IN FINITE DIFFERENCE FORMULAS which explains how the weigths are to be calculated in the one dimensional case .

I couldn't find a similar reference for the twodimensional case.

My question:

  • How is the differentiationMatrix evaluated in this case, especially at boundary meshpoints?
  • Are there additional helpful references in the Mathematica documentation?

Thanks!