scholarly journals RESTRICTIVE PADE' APPROXIMATION FOR SOLVING SINGULARLY PERTURBED INITIAL BOUNDARY VALUE PROBLEM FOR HYPERBOLIC PARTIAL DIFFERENTIAL EQUATION

2001 ◽  
Vol 9 (ASAT CONFERENCE) ◽  
pp. 1-9
Author(s):  
Hassan Ismail ◽  
Adel Elmekkawy
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Singularly Perturbed ◽  
Hyperbolic Partial Differential Equation ◽  
Partial Differential ◽  
Initial Boundary Value

Existence Theorem for the Initial-Boundary Value Problem for a Singular Parabolic Partial Differential Equation

1972 ◽  
Vol 15 (2) ◽  
pp. 229-234
Author(s):  
Julius A. Krantzberg
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Parabolic Partial Differential Equation ◽  
Partial Differential ◽  
Image Position ◽  
Initial Boundary Value

We consider the initial-boundary value problem for the parabolic partial differential equation1.1in the bounded domain D, contained in the upper half of the xy-plane, where a part of the x-axis lies on the boundary B(see Fig.1).

Numerical Method for Singularly Perturbed Parabolic Equations in Unbounded Domains in the Case of Solutions Growing at Infinity

2009 ◽  
Vol 9 (1) ◽  
pp. 100-110
Author(s):  
G. I. Shishkin
Keyword(s):  
Boundary Layer ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Singularly Perturbed ◽  
Reaction Diffusion Equation ◽  
Maximum Norm ◽  
Lateral Part ◽  
Initial Boundary Value

AbstractAn initial-boundary value problem is considered in an unbounded do- main on the x-axis for a singularly perturbed parabolic reaction-diffusion equation. For small values of the parameter ε, a parabolic boundary layer arises in a neighbourhood of the lateral part of the boundary. In this problem, the error of a discrete solution in the maximum norm grows without bound even for fixed values of the parameter ε. In the present paper, the proximity of solutions of the initial-boundary value problem and of its numerical approximations is considered. Using the method of special grids condensing in a neighbourhood of the boundary layer, a special finite difference scheme converging ε-uniformly in the weight maximum norm has been constructed.

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