By using sufficient conditions which ensure the well conditioning of tridiagonal matrices, we derive numerical methods for second order singular perturbations boundary values problems. Under hypotheses similar to the ones usually used in the continuous theory, methods are derived which use constant step sizes h almost-equal-to O (epsilon(1/2)). In the more general case methods with variable step sizes, are defined which solve the problem with n(<< epsilon-1) steps. Examples on standard test problems are shown.
NUMERICAL-METHODS FOR 2ND-ORDER SINGULAR PERTURBATION PROBLEMS
MAZZIA, Francesca;
1992-01-01
Abstract
By using sufficient conditions which ensure the well conditioning of tridiagonal matrices, we derive numerical methods for second order singular perturbations boundary values problems. Under hypotheses similar to the ones usually used in the continuous theory, methods are derived which use constant step sizes h almost-equal-to O (epsilon(1/2)). In the more general case methods with variable step sizes, are defined which solve the problem with n(<< epsilon-1) steps. Examples on standard test problems are shown.File in questo prodotto:
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