Some stable difference approximations to a fourth-order parabolic partial differential equation

Abstract

Consider the fourth-order parabolic partial differential equation subject to the initial conditions u(x, 0) = g0(x) (lb) du -(x, 0) = gi(x) for 0 ^ x ^ 1, and the boundary conditions «(0,0 =/o(0, «(1, t) = hit), 0(O,i) =Po(0, g(l,i) =Pi(0, Following Richtmyer [11] we introduce two new variables $ and SF defined by (2) $ = -, V = -.y !dt ' dx* Eq. (la) can now be rewritten as two simultaneous partial differential equations of the form , .d$ _ _a*¥ r)^ _ r)2í>