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CONVERGENCE CONSISTENCY AND STABILITY
SOLVING THE ONEDIMENSIONAL DIFFUSION EQUATION
28 other sections not shown
accuracy algebraic equations amplitude analysis applied boundary conditions boundary element method boundary values Burgers calculated Chebyshev coefficients considered constant convergence coordinate Crank-Nicolson Crank-Nicolson method diagonal differencing discretisation error displacements eigenvalues elimination entries evaluated exact solution example Figure finite difference approximation finite difference equation finite difference method finite element method flow fluid formulation Fourier FTCS method Galerkin method Gaussian elimination given gives gradient grid spacing grid-point implicit method initial conditions integral equation iterative methods linear algebraic mathematical matrix Neumann nodal nodes non-zero nonlinear Numerical Methods numerical solution obtained parameters partial differential equation polynomial problem propagation Reynolds number Section shape functions shock solved sparse sparse matrix spectral method stability step symmetric system of equations Taylor series techniques Thomas algorithm traditional Galerkin method transformation transport equation tridiagonal truncation error two-dimensional upwind variable vector velocity wave zero