Solving a partially singularly perturbed initial value problem on Shishkin meshes

Meenakshi, P. Maragatha; Sigamani, Valarmathi; Miller, John J. H.

doi:10.1016/j.amc.2009.09.038

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Cited by 8 publications

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Numerical Solution for a Coupled System of Singularly Perturbed Initial Value Problems with Discontinuous Source Term

Rao

Chawla

2015

Springer Proceedings in Mathematics &Amp; Statistics

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In this work, we study a numerical method for a coupled system of singularly perturbed initial value problems having discontinuous source term. The leading term of each equation is multiplied by a distinct small positive parameter, due to which the overlapping initial and interior layers are generated in the solution. The problem is discretized using backward Euler difference scheme which involves an appropriate piecewise-uniform variant of Shishkin mesh that is fitted to both the initial and interior layers. The method is proved to be uniformly almost first-order accurate with respect to all the parameters. Numerical results are presented in support of the theory.

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Numerical Solution for a Coupled System of Singularly Perturbed Initial Value Problems with Discontinuous Source Term

Rao

Chawla

2015

Springer Proceedings in Mathematics &Amp; Statistics

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Parameter-robust numerical method for a system of singularly perturbed initial value problems

Kumar

2011

Numer Algor

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In this work we study a system of M(≥ 2) first-order singularly perturbed ordinary differential equations with given initial conditions. The leading term of each equation is multiplied by a distinct small positive parameter, which induces overlapping layers. A maximum principle does not, in general, hold for this system. It is discretized using backward Euler difference scheme for which a general convergence result is derived that allows to establish nodal convergence of O(N −1 ln N) on the Shishkin mesh and O(N −1 ) on the Bakhvalov mesh, where N is the number of mesh intervals and the convergence is robust in all of the parameters. Numerical experiments are performed to support the theoretical results.

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Analysis of some numerical methods on layer adapted meshes for singularly perturbed quasilinear systems

Kumar

2015

Numer Algor

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Solving a partially singularly perturbed initial value problem on Shishkin meshes

Cited by 8 publications

References 3 publications

Numerical Solution for a Coupled System of Singularly Perturbed Initial Value Problems with Discontinuous Source Term

Numerical Solution for a Coupled System of Singularly Perturbed Initial Value Problems with Discontinuous Source Term

Parameter-robust numerical method for a system of singularly perturbed initial value problems

Analysis of some numerical methods on layer adapted meshes for singularly perturbed quasilinear systems

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