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Chapter 2 Finite Difference Techniques for Partial Differential Equations
Chapter 4 The Finite Element Method in Engineering Application
absolute stability accuracy algebraic equations algorithm amplification factor amplitude analysis applied boundary conditions Boundary Element Methods boundary values Burgers calculated central difference coefficients considered convection equation convergence coordinate Crank-Nicolson Crank-Nicolson method derivative diagonal discretisation error eigenvalues estimate Euler's method evaluated exact solution example explicit extrapolation Figure finite difference approximation finite difference equation finite difference method finite element method Fletcher flow fluid formulation FTCS method Galerkin method given gives grid spacing gridpoints implicit method initial condition initial value problem iterative methods mathematical Neumann nodes non-zero nonlinear numerical method numerical solution obtained Ordinary Differential Equations parameters partial differential equation polynomial region Runge-Kutta methods satisfy Section shape functions shown sparse spatial spectral step length subroutine Substitution symmetric Taylor series techniques transport equation trial functions trial solution truncation error upwind variable vector velocity zero