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INTRODUCTION TO DISCRETE VARIABLE METHODS
Dr A Prothero Chapters 9
CONVERGENCE AND STABILITY
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A-stable absolute stability accuracy Adams methods algorithm applied approximate solution asymptotic boundary conditions boundary value problems calculation Chapter coefficients collocation computed consider constant convergence corrector defined delay equations derivative described discretization error discussed efficient eigenvalues Enright equation 1.1 error estimate evaluations example explicit extrapolation finite difference function Gear given global error implementation implicit methods implicit Runge-Kutta initial value problem integration interpolation inverse iteration Jacobian matrix Krogh Lindberg linear multistep methods Math methods for stiff Newton's method nonlinear equations numerical methods numerical solution obtain one-step methods order equations ordinary differential equations parameters perturbation polynomial predictor range region of absolute Rept root Runge-Kutta methods satisfy shooting method singular solving stability properties stability region starting values step length stepsize stiff differential equations stiff problems stiff systems system of equations techniques Theorem trapezium rule truncation error updating variable step vector zero zero-stable