Abstract
This paper is concerned with the numerical solution for singular perturbation system of two coupled second ordinary differential equations with initial and boundary conditions, respectively. Fitted finite difference scheme on a uniform mesh, whose solution converges pointwise independently of the singular perturbation parameter is constructed and analyzed.
Highlights
We consider the following singularly perturbed initial/boundary value problem for the linear system of ordinary differential equations in the interval 0,1 : (1)c1 x v x f1 x, L2u : v x a2 x v x (2)c2 x u x f2 x, u 0 A1, u 0 B1 (3) (4)where 0 is a small parameter, 0, A1, A2, B1, The above type initial/boundary value problems arise in many areas of mechanics and physics [1,2].Differential equations with a small parameter multiplying the highest order derivative terms are said to be singularly perturbed and normally boundary layers occur in their solutions
This paper is concerned with the numerical solution for singular perturbation system of two coupled second ordinary differential equations with initial and boundary conditions, respectively
It is important to develop suitable numerical methods to these problems, whose accuracy does not depend on the parameter value, i.e. methods that are -uniformly convergent
Summary
The above type initial/boundary value problems arise in many areas of mechanics and physics [1,2]. It is important to develop suitable numerical methods to these problems, whose accuracy does not depend on the parameter value , i.e. methods that are -uniformly convergent These include fitted finite difference methods, finite element methods using special elements such as exponential elements, and methods which use a priori refined or special non-uniform grids which condense in the boundary layers in a special manner. The various approaches to the design and analysis of appropriate numerical methods for singularly perturbed differential equations can be found in [3,4,5,6,7,8] (see references cited in them) In this present paper, we analyze the numerical solution of the initial/boundary problems (1)-(4). Throughout the paper, C will denote a generic positive constant independent of and of the mesh parameter
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
