A Fast Adaptive Numerical Method for Stiff Two-Point Boundary Value Problems

Authors:
June-Yub Lee;Leslie Greengard
Affiliations:
-;-
Venue:
SIAM Journal on Scientific Computing
Year:
1997

Citing 0
Cited 11

A survey of numerical techniques for solving singularly perturbed ordinary differential equations

Applied Mathematics and Computation
Fast Stable Solver for Sequentially Semi-separable Linear Systems of Equations

HiPC '02 Proceedings of the 9th International Conference on High Performance Computing
Optimized point shifts and poles in the linear rational pseudospectral method for boundary value problems

Journal of Computational Physics
A Fourier-Wachspress method for solving Helmholtz's equation in three-dimensional layered domains

Journal of Computational Physics
A Fourier-Wachspress method for solving Helmholtz's equation in three-dimensional layered domains

Journal of Computational Physics
Adaptive multiquadric collocation for boundary layer problems

Journal of Computational and Applied Mathematics
Numerical methods for solving moment equations in kinetic theory of neuronal network dynamics

Journal of Computational Physics
Krylov deferred correction accelerated method of lines transpose for parabolic problems

Journal of Computational Physics
Fredholm integral equation method for the integro-differential Schrödinger equation

Computers & Mathematics with Applications
Adaptive multiquadric collocation for boundary layer problems

Journal of Computational and Applied Mathematics
A Bootstrap Method for Sum-of-Poles Approximations

Journal of Scientific Computing

Quantified Score

Hi-index	0.03

Visualization

Abstract

We describe a robust, adaptive algorithm for the solution of singularly perturbed two-point boundary value problems. Many different phenomena can arise in such problems, including boundary layers, dense oscillations, and complicated or ill-conditioned internal transition regions. Working with an integral equation reformulation of the original differential equation, we introduce a method for error analysis which can be used for mesh refinement even when the solution computed on the current mesh is underresolved. Based on this method, we have constructed a black-box code for stiff problems which automatically generates an adaptive mesh resolving all features of the solution. The solver is direct and of arbitrarily high-order accuracy and requires an amount of time proportional to the number of grid points.