Numerical solution of nonlinear singularly perturbed problems by using a non-standard algorithm on variable stepsize implementation (CMMSE–2009)

In this article, we solve numerically singularly perturbed non-linear autonomous initial-value problems (IVPs) by using a non-standard algorithm on a variable stepsize implementation. On a recent article (Ramos et al. in J Math Chem, To appear) we had used nonuniform meshes for resolving the difficu...

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Bibliographic Details
Published in:Journal of mathematical chemistry Vol. 48; no. 1; pp. 98 - 108
Main Authors: Ramos, Higinio, García-Rubio, R.
Format: Journal Article Conference Proceeding
Language:English
Published: Dordrecht Springer Netherlands 01.07.2010
Springer
Subjects:
Chemistry
Chemistry and Materials Science
Exact sciences and technology
General and physical chemistry
Math. Applications in Chemistry
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Original Paper
Partial differential equations
Partial differential equations, initial value problems and time-dependant initial-boundary value problems
Physical Chemistry
Sciences and techniques of general use
Theoretical and Computational Chemistry
Theory of reactions, general kinetics. Catalysis. Nomenclature, chemical documentation, computer chemistry
Nonuniform meshes
Singularly perturbed initial-value problems
Non-standard algorithm
Variable stepsize implementation
Mathematical chemistry
Grid pattern
Initial value problem
Nonlinear problems
Algorithm
Layer
Implementation
Standards
Efficiency
Numerical solution
Singularly perturbed initial-value problem
Problem solving
ISSN:0259-9791, 1572-8897
Online Access:Get full text
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Summary:In this article, we solve numerically singularly perturbed non-linear autonomous initial-value problems (IVPs) by using a non-standard algorithm on a variable stepsize implementation. On a recent article (Ramos et al. in J Math Chem, To appear) we had used nonuniform meshes for resolving the difficulties arising from the steep gradient of the solution in the initial layer. The present method is intended for solving the nonlinear problem using a nonuniform mesh originated by a suitable strategy provided for changing the stepsize. Numerical experiments are carried out to verify the efficiency and accuracy of the method, showing that the new procedure leads to better results than in (Ramos et al. in J Math Chem, To appear).
ISSN:0259-9791
1572-8897
DOI:10.1007/s10910-009-9636-z