A class of alternating group explicit finite difference method for diffusion equation
Using six grid points, the author constructs an implicit finite difference scheme with parameters for the diffusion problem \({\partial u\over\partial t}= a{\partial^2 u\over\partial x^2}\), \(u(x,0)= f(x)\), \(u(0,t)= g_1(t)\), \(u(1,t)= g_2(t)\) on the rectangle \([0,1]\times [0,T]\). Choosing adequately the parameters one obtains the truncation error \(O(\tau^2+ h^4)\) of the scheme, where \(\tau\) and \(h\) are temporal and spatial step sizes, respectively. Next four asymmetry difference schemes are presented and based on them a class of alternating group explicit method is proposed. It is proved unconditionally stability (so by Lax theorem also convergence) to the method. Two numerical examples demonstrates high accuracy of the method.
alternating group explicit finite difference method
scientific article; zbMATH DE number 5606219