A HYBRID DIFFERENCE SCHEME FOR SINGULARLY PERTURBED SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS WITH DISCONTINUOUS CONVECTION COEFFICIENT AND MIXED TYPE BOUNDARY CONDITIONS

This paper presents, a hybrid difference scheme for singularly perturbed second order ordinary differential equations with a small parameter multiplying the highest derivative with a discontinuous convection coefficient subject to mixed type boundary conditions. Error bounds for the numerical solution and numerical derivative are established. Numerical results are provided to illustrate the theoretical results.

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Mixed-type boundary conditions for second order elliptic differential equations

Journal of the Mathematical Society of Japan ◽

10.2969/jmsj/02630405 ◽

1974 ◽

Vol 26 (3) ◽

pp. 405-432 ◽

Cited By ~ 7

Author(s):

Yoshio KATO

Keyword(s):

Differential Equations ◽

Boundary Conditions ◽

Mixed Type ◽

Second Order ◽

Elliptic Differential Equations ◽

Type Boundary

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UNIFORMLY-CONVERGENT NUMERICAL METHODS FOR A SYSTEM OF COUPLED SINGULARLY PERTURBED CONVECTION–DIFFUSION EQUATIONS WITH MIXED TYPE BOUNDARY CONDITIONS

Mathematical Modelling and Analysis ◽

10.3846/13926292.2013.851629 ◽

2013 ◽

Vol 18 (5) ◽

pp. 557-598 ◽

Cited By ~ 5

Author(s):

Rajarammohanroy Mythili Priyadharshini ◽

Narashimhan Ramanujam

Keyword(s):

Boundary Conditions ◽

Mixed Type ◽

Coupled System ◽

Second Order ◽

Singularly Perturbed ◽

Supremum Norm ◽

Convection Diffusion ◽

Weakly Coupled System ◽

Type Boundary ◽

Second Order Convergence

In this paper, two hybrid difference schemes on the Shishkin mesh are constructed for solving a weakly coupled system of two singularly perturbed convection - diffusion second order ordinary differential equations subject to the mixed type boundary conditions. We prove that the method has almost second order convergence in the supremum norm independent of the diffusion parameter. Error bounds for the numerical solution and also the numerical derivative are established. Numerical results are provided to illustrate the theoretical results.

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SINGULARLY PERTURBED BOUNDARY VALUE PROBLEMS FOR SECOND ORDER NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS HAVING WEAKLY DISCONTINUOUS REDUCED SOLUTIONS

Acta Mathematica Scientia ◽

10.1016/s0252-9602(18)30303-5 ◽

1988 ◽

Vol 8 (3) ◽

pp. 239-248 ◽

Cited By ~ 2

Author(s):

Weili Zhao

Keyword(s):

Differential Equations ◽

Ordinary Differential Equations ◽

Boundary Value Problems ◽

Boundary Value ◽

Second Order ◽

Singularly Perturbed ◽

Nonlinear Ordinary Differential Equations

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Initial-Value Technique for Singularly Perturbed Boundary-Value Problems for Second-Order Ordinary Differential Equations Arising in Chemical Reactor Theory

Journal of Optimization Theory and Applications ◽

10.1023/a:1022639003366 ◽

1998 ◽

Vol 97 (2) ◽

pp. 455-470 ◽

Cited By ~ 18

Author(s):

S. Natesan ◽

N. Ramanujam

Keyword(s):

Differential Equations ◽

Ordinary Differential Equations ◽

Boundary Value Problems ◽

Boundary Value ◽

Chemical Reactor ◽

Second Order ◽

Singularly Perturbed ◽

Initial Value

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High-Order Method for a Singularly Perturbed Second-Order Ordinary Differential Equation with Discontinuous Source Term Subject to Mixed Type Boundary Conditions

Mathematical Modelling and Scientific Computation - Communications in Computer and Information Science ◽

10.1007/978-3-642-28926-2_38 ◽

2012 ◽

pp. 351-359 ◽

Cited By ~ 1

Author(s):

R. Mythili Priyadharshini ◽

N. Ramanujam

Keyword(s):

Differential Equation ◽

Ordinary Differential Equation ◽

Boundary Conditions ◽

Mixed Type ◽

Source Term ◽

Singularly Perturbed ◽

Order Method ◽

High Order Method ◽

Discontinuous Source Term ◽

Type Boundary

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Asymptotic initial value methods for two-parameter singularly perturbed boundary value problems for second order ordinary differential equations

Applied Mathematics and Computation ◽

10.1016/s0096-3003(02)00160-1 ◽

2003 ◽

Vol 137 (2-3) ◽

pp. 549-570 ◽

Cited By ~ 6

Author(s):

T. Valanarasu ◽

N. Ramanujam

Keyword(s):

Differential Equations ◽

Ordinary Differential Equations ◽

Boundary Value Problems ◽

Boundary Value ◽

Second Order ◽

Singularly Perturbed ◽

Initial Value ◽

Two Parameter

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Existence theory for coupled nonlinear third-order ordinary differential equations with nonlocal multi-point anti-periodic type boundary conditions on an arbitrary domain

AIMS Mathematics ◽

10.3934/math.2019.6.1634 ◽

2019 ◽

Vol 4 (6) ◽

pp. 1634-1663

Author(s):

Bashir Ahmad ◽

◽

Ahmed Alsaedi ◽

Mona Alsulami ◽

Sotiris K. Ntouyas ◽

...

Keyword(s):

Differential Equations ◽

Boundary Conditions ◽

Ordinary Differential Equations ◽

Existence Theory ◽

Arbitrary Domain ◽

Third Order ◽

Type Boundary

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The interlacing of eigenvalues for periodic multi-parameter problems

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s0308210500010350 ◽

1978 ◽

Vol 80 (3-4) ◽

pp. 357-362 ◽

Cited By ~ 4

Author(s):

Patrick J. Browne

Keyword(s):

Differential Equations ◽

Boundary Conditions ◽

Ordinary Differential Equations ◽

Periodic Boundary ◽

Eigenvalue Problems ◽

Periodic Boundary Conditions ◽

Second Order ◽

Image Position ◽

Periodic Equation

SynopsisThis paper studies a linked system of second order ordinary differential equationswhere xx ∈ [ar, br] and the coefficients qrars are continuous, real valued and periodic of period (br − ar), 1 ≤ r,s ≤ k. We assume the definiteness condition det{ars(xr)} > 0 and 2k possible multiparameter eigenvalue problems are then formulated according as periodic or semi-periodic boundary conditions are imposed on each of the equations of (*). The main result describes the interlacing of the 2k possible sets of eigentuples thus extending to the multiparameter case the well known theorem concerning 1-parameter periodic equation.

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