A fast adaptive numerical method for stiff two-point boundary value problems

Journal Article · Sat Mar 01 04:00:00 EST 1997 · SIAM Journal on Scientific Computing

DOI:https://doi.org/10.1137/S1064827594272797· OSTI ID:471153

Lee, J Y; Greengard, L ^[1]

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1. New York Univ., NY (United States). Courant Inst. of Mathematical Sciences

The authors 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, the authors 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, they 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.

• Sponsoring Organization: USDOE, Washington, DC (United States)
• DOE Contract Number: FG02-88ER25053
• OSTI ID: 471153
• Journal Information: SIAM Journal on Scientific Computing, Journal Name: SIAM Journal on Scientific Computing Journal Issue: 2 Vol. 18; ISSN 1064-8275; ISSN SJOCE3
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
ALGORITHMS
BOUNDARY-VALUE PROBLEMS
INTEGRAL EQUATIONS
MESH GENERATION
NUMERICAL SOLUTION