Abstract
This chapter discusses the solution of numerical solution of differential equations in two or more independent variables—partial differential equations. Like ordinary differential equations, a solution of a differential equation is not determined without appropriate initial and/or boundary conditions, and the same is expected to be true for partial differential equation. There are several variations on this problem that can be modeled by changing the boundary conditions or the equation itself. The chapter focuses on techniques for the numerical solution of problems. There is a classical analytical technique for representing the solution by means of Fourier series. This technique is valid only under very restrictive conditions, but it does apply to the heat and wave equations together with the types of initial and boundary conditions. The method of separation of variables together with the use of Fourier series is a classical technique for solving certain simple equations.
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