Abstract
In this study, we developed a solution of nonhomogeneous heat equation with Dirichlet boundary conditions. moreover, the non-homogeneous heat equation with constant coefficient. since heat equation has a simple form, we would like to start from the heat equation to find the exact solution of the partial differential equation with constant coefficient. to emphasize our main results, we also consider some important way of solving of partial differential equation specially solving heat equation with Dirichlet boundary conditions. the main results of our paper are quite general in nature and yield some interesting solution of non-homogeneous heat equation with Dirichlet boundary conditions and it is used for problems of mathematical modeling and mathematical physics.
Highlights
IntroductionDifferential equations are used to construct more models of reality and these modeling suggests that some solutions of the differential equations with variable coefficients using different methods There are more methods of solving different researchers applied to solve heat equation by different method in this paper we find a solution of nonhomogeneous heat equation with Dirichlet Boundary conditions
Differential equations are used to construct more models of reality and these modeling suggests that some solutions of the differential equations with variable coefficients using different methods There are more methods of solving different researchers applied to solve heat equation by different method in this paper we find a solution of nonhomogeneous heat equation with Dirichlet Boundary conditions.Many physical problems such as wave equation, heat equation, Poisson equation and Laplace equation are modeled by differential equations which are an example of partial differential equations. some partial differential equations have numerical solution and exact solution in regular shape domain but in this paper, we will try to solve exact solution of non-homogeneous heat equation
There are special solutions to the heat equation which are sufficiently fundamental that solutions to very broad categories of heat conduction problems can be written immediately in terms of these fundamental solutions to the differential equation
Summary
Differential equations are used to construct more models of reality and these modeling suggests that some solutions of the differential equations with variable coefficients using different methods There are more methods of solving different researchers applied to solve heat equation by different method in this paper we find a solution of nonhomogeneous heat equation with Dirichlet Boundary conditions. Many physical problems such as wave equation, heat equation, Poisson equation and Laplace equation are modeled by differential equations which are an example of partial differential equations. When we solving a partial differential equation, we will need initial or boundary value problems to get the particular solution of the partial differential equation
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