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FFT Solution of Partial Differential Equations
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5-point applied approximation assume Buzbee calculation capacitance capacity matrix Chapter coefficient complex components compute Concus conjugate corresponding cyclic reduction defined denotes derived described difference equations Dirichlet boundary conditions Dirichlet conditions Dirichlet problem discrete Poisson equation discussion efficient eigenvalues eigenvectors eliminated equations elliptic problems evaluation example exponential scheme factor Fast Fourier Transform fast solvers FFT algorithm FFT methods FFT techniques finite finite-difference formula Fortran Fourier analysis Fourier harmonics Fourier series Furthermore given grid points Hence Hockney Hockney's Huntley indicated iteration Laplace transform linear equations matrix factorisation matrix of order maximum modulus error mesh multiplications numerical solution obtain operation count overall parabolic partial differential equations Phys Pickering Poisson problem Poisson's equation Proskurowski rectangle rectangular region reduction procedure relation relevant respectively right-hand side Section solution of Poisson's subsidiary equation suitable systems of equations tridiagonal matrix tridiagonal systems usual values vectors Widlund written