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Chapter 2 Finite Difference Techniques for Partial Differential Equations
Chapter 3 The Galekin Method and Burgers Equation
Chapter 4 The Finite Element Method in Engineering Application
Chapter 5 An Introduction to the Boundary Element Method
Chapter 6 Direct Solution and Storage of Large Sparse Linear Systems
Chapter 7 Iterative Methods for Solving Large Sparse Systems of Linear Algebraic Equations ...
absolute stability accuracy algebraic equations algorithm amplitude analysis applied boundary conditions Boundary Element Methods boundary values Burgers calculated central difference Chebyshev coefficients considered convection equation convergence coordinate Crank-Nicolson Crank-Nicolson method derivative diagonal discretisation error eigenvalues 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 finite implicit method initial condition initial value problem iterative methods mathematical matrix nodes non-zero nonlinear Numerical Methods numerical solution obtained one-dimensional diffusion equation Ordinary Differential Equations parameters partial differential equation polynomial region Reynolds number Runge-Kutta methods Section shown sparse sparse matrix spatial step length subroutine symmetric Table Taylor series techniques transport equation trial functions trial solution truncation error upwind variable vector zero