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

From MaRDI portal
Publication:1855755

DOI10.1016/S0096-3003(01)00112-6zbMath1026.65059OpenAlexW1964642962MaRDI QIDQ1855755

Mohan K. Kadalbajoo, Kailash C. Patidar

Publication date: 28 January 2003

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0096-3003(01)00112-6




Related Items (56)

Solving Volterra integro-differential equations by variable stepsize block BS methods: properties and implementation techniquesHigh order parameter uniform numerical method for singular perturbation problemsA rational spectral collocation method for third-order singularly perturbed problemsOn the multiple scales perturbation method for difference equations\(\epsilon\) -uniformly convergent fitted methods for the numerical solution of the problems arising from singularly perturbed general ddesPiecewise approximate analytical solutions of high-order singular perturbation problems with a discontinuous source termA comparison between MMAE and SCEM for solving singularly perturbed linear boundary layer problemsNon-standard methods for singularly perturbed problems possessing oscillatory/layer solutionsSolution of dual boundary layer singular perturbation problem by septic Hermite collocation techniqueA brief survey on numerical methods for solving singularly perturbed problemsAn equidistributed grid-based second-order scheme for a singularly perturbed Fredholm integro-differential equation with an interior layerStudy of Self-Adjoint Singularly Perturbed BVP by Septic Hermite Collocation MethodA non-uniform Haar wavelet method for a singularly perturbed convection-diffusion type problem with integral boundary condition on an exponentially graded meshAn almost second-order robust computational technique for singularly perturbed parabolic turning point problem with an interior layerAn efficient numerical technique for two-parameter singularly perturbed problems having discontinuity in convection coefficient and source termNumerical solution of a fourth‐order singularly perturbed boundary value problem with discontinuities via Haar waveletsThe Lie-group shooting method for solving nonlinear singularly perturbed boundary value problemsRational spectral collocation combined with singularity separation method for second-order singular perturbation problemsA numerical approach for singular perturbation problems with an interior layer using an adaptive splineCoupling of high order multiplication perturbation method and reduction method for variable coefficient singular perturbation problemsA uniformly convergent finite difference scheme for Robin type singularly perturbed parabolic convection diffusion problemA review on singularly perturbed differential equations with turning points and interior layersUniform global convergence of a hybrid scheme for singularly perturbed reaction-diffusion systemsA robust fitted operator finite difference method for a two-parameter singular perturbation problem1First asymptotic approximations to a solution of singularly perturbed optimal control problem with intersecting solutions of degenerate problemAsymptotic solution of a singularly perturbed optimal problem with integral constraintSextic spline solution of a singularly perturbed boundary-value problemExperiments with a local adaptive grid \(h\)-refinement for the finite-difference solution of BVPs in singularly perturbed second-order ODEsUnnamed ItemHigh-order exponentially fitted difference schemes for singularly perturbed two-point boundary value problemsNon-polynomial spline solution of singularly perturbed boundary-value problemsParameter-uniform finite difference scheme for a system of coupled singularly perturbed convection–diffusion equationsA robust fitted operator finite difference method for singularly perturbed problems whose solution has an interior layerHigh order robust approximations for singularly perturbed semilinear systemsAdaptive solution of BVPs in singularly perturbed second-order ODEs, by the extended Numerov method combined with an iterative local grid \(h\)-refinementHigh order parameter-robust numerical method for singularly perturbed reaction-diffusion problemsSingularly perturbed differential equations with discontinuous coefficients and concentrated factorsA recent survey on computational techniques for solving singularly perturbed boundary value problemsA general method for solving singular perturbed impulsive differential equations with two-point boundary conditionsA finite difference method for the singularly perturbed problem with nonlocal boundary conditionChebyshev solution of the nearly-singular one-dimensional Helmholtz equation and related singular perturbation equations: multiple scale series and the boundary layer rule-of-thumbAn efficient dynamical systems method for solving singularly perturbed integral equations with noise\(\varepsilon\)-uniformly convergent fitted mesh finite difference methods for general singular perturbation problemsComputational approach for fourth-order self-adjoint singularly perturbed boundary value problems via non-polynomial quintic splineA robust layer-resolving spline collocation method for a convection-diffusion problemHigh-order Gegenbauer integral spectral element method integrated with an adaptive Chebyshev optimization strategy for solving linear singularly perturbed differential equationsA robust fitted numerical method for singularly perturbed turning point problems whose solution exhibits an interior layerRational spectral collocation combined with the singularity separated method for a system of singularly perturbed boundary value problemsA uniformly convergent nonstandard finite difference scheme for a system of convection-diffusion equationsBernstein operator method for approximate solution of singularly perturbed Volterra integral equationsAsymptotic approximation to a solution of a singularly perturbed linear-quadratic optimal control problem with second-order linear ordinary differential equation of state variableA recent development of computer methods for solving singularly perturbed boundary value problemsSolving singularly perturbed problems by a weak-form integral equation with exponential trial functionsNumerical Solution of Singularly Perturbed Two-point BVPs Using Nonuniform Haar WaveletsA new way to generate an exponential finite difference scheme for 2D convection-diffusion equationsHigh order fitted operator numerical method for self-adjoint singular perturbation problems


Uses Software


Cites Work


This page was built for publication: A survey of numerical techniques for solving singularly perturbed ordinary differential equations