Abstract
In this paper two dimensional parabolic equation with Dirichlettype boundary condition is considered. The existence and uniqueness of solution are shown. Also we construct an iteration algorithm for the numericalsolution of this problem
Highlights
Consider the following mixed problem: @u @2u @2u@t = @x2 + @y2 + f (x; y; t) ; (1) (x; y; t): = f0 < x < ; 0 < y < ; 0 < t < T g u(0; y; t) = u( ; y; t) = 0 ; t [0; T ] (2)u(x; 0; t) = u(x; ; t) = 0 ; t [0; T ] (3)u(x; y; 0) = '(x; y) ; x [0; ]
The description of various numerical and other methods with useful bibliography may be found in the surveys of [8, 2, 3] .Compact di¤erence scheme for solving wave equations in two-space dimensions is discussed in [4]
In this study we prove the existence,uniqueness of the solution and we constract an iteration algorithm for the numerical solution
Summary
The description of various numerical and other methods with useful bibliography may be found in the surveys of [8, 2, 3] .Compact di¤erence scheme for solving wave equations in two-space dimensions is discussed in [4]. In this study we prove the existence,uniqueness of the solution and we constract an iteration algorithm for the numerical solution. We will use Fourier method for the considered problem (1)-(4).
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