Abstract
This work deals with a second order linear general equation with partial derivatives for a two-variable function. It covers a wide range of applications. This equation is solved with a finite difference hybrid method: BTCS + CTCS. This scheme is simple, precise, and economical in terms of time and space occupancy in memory.
Highlights
This work deals with a second order linear general equation with partial derivatives for a two-variable function
∂ t where Φ designates an scalar function depending on the variables x and t
We propose to solve this equation with a simple, accurate and efficient method, by reducing the costs in time, memory space, and method’s heaviness
Summary
We consider a scalar function Φ = Φ ( x,t ) which depends on the real variables x and t. We superpose the two approaches in order to obtain a better approximation of the solution of the treated differential equation. In this way we combine the advantages of the two schemes. We obtain the following matrix equation, considering the mesh points x1 and xNx : d1 e1 0. We will discuss the inversion methods of the matrix ( A)n , which permits to get the solution Φn
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