Exact finite-difference schemes for two-dimensional linear systems with constant coefficients

✍ Scribed by Lih-Ing W. Roeger

• Publisher: Elsevier Science
• Year: 2008
• Tongue: English
• Weight: 144 KB
• Volume: 219
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/j.cam.2007.07.015

✦ Synopsis

An exact finite-difference scheme for a system of two linear differential equations with constant coefficients, (d/dt)x(t) = Ax(t), is proposed. The scheme is different from what was proposed by Mickens [Nonstandard Finite Difference Models of Differential Equations, World Scientific, New Jersey, 1994, p. 147], in which the derivatives of the two equations are formed differently. Our exact scheme is in the form of (1/(h))(x k+1x k ) = A[ x k+1 + (1 -)x k ]; both derivatives are in the same form of (x k+1x k )/(h).