TEXTS IN APPLIED MATHEMATICS, 52

By DONALD CLARK

CONTENTS INITIAL VALUE PROBLEMS INTRODUCTION EXAMPLES OF IVPS METHODS OBTAINED FROM NUMERICAL DI?ERENTIATION THE FIVE STEPS ADDITIONAL DI?ERENCE METHODS METHODS OBTAINED FROM NUMERICAL QUADRATURE RUNGE–KUTTA METHODS EXTENSIONS AND GHOST POINTS CONSERVATIVE METHODS VELOCITY VERLET SYMPLECTIC METHODS NEXT STEPS EXERCISES TWO-POINT BOUNDARY VALUE PROBLEMS BIRDS ON A WIRE CHEMICAL KINETICS DERIVATIVE APPROXIMATION METHODS MATRIX PROBLEM TRIDIAGONAL MATRICES MATRIX PROBLEM REVISITED ERROR ANALYSIS EXTENSIONS RESIDUAL METHODS BASIS FUNCTIONS RESIDUAL SHOOTING METHODS DI?USION PROBLEMS HEAT EQUATION IMPLICIT METHOD THETA METHOD CRANK–NICOLSON METHOD L-STABILITY METHODS OF LINES COLLOCATION ADVECTION EQUATION METHOD OF CHARACTERISTICS SOLUTION PROPERTIES BOUNDARY CONDITIONS FIRST-ORDER METHODS UPWIND SCHEME DOWNWIND SCHEME NUMERICAL DOMAIN OF DEPENDENCE STABILITY IMPROVEMENTS LAX–WENDRO?METHOD MONOTONE METHODS UPWIND REVISITED IMPLICIT METHODS NUMERICAL WAVE PROPAGATION SOLUTION METHODS PLANE WAVE SOLUTIONS EXPLICIT METHOD DIAGNOSTICS NUMERICAL EXPERIMENTS NUMERICAL PLANE WAVES NUMERICAL GROUP VELOCITY ELLIPTIC PROBLEMS SOLUTIONS PROPERTIES OF THE SOLUTION FINITE DI?ERENCE APPROXIMATION BUILDING THE MATRIX POSITIVE DE?NITE MATRICES DESCENT METHODS STEEPEST DESCENT METHOD CONJUGATE GRADIENT METHOD NUMERICAL SOLUTION OF LAPLACE’S EQUATION PRECONDITIONED CONJUGATE GRADIENT METHOD