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

Some Stable Difference Approximations to a Fourth-Order Parabolic Partial Differential Equation

where £i = * and A = 0 -11 .1 o J' Since A AA' = 0 and A'1 = —A, (4) is a Schrodinger type system of partial differential equations, (Kreiss [6]). Richtmyer [11] and Evans [5] have derived finite difference methods for the numerical solution of Eq. (4) which are based on well-known algorithms for the numerical solution of the scalar equation , _. dv _ d"v {ö) Tt~dx~*Received February 21, 1966.

Quasi - wavelet for Fourth Order Parabolic Partial Integro - differential Equation ⋆

In this paper we discuss the numerical solution of initial-boundary value problem for the fourth order parabolic partial integro-differential equation. We use the forward Euler scheme for time discretization and the quasi-wavelet method for space discretization. Sometimes, we give a new method about the treatment of boundary condition. Numerical experiment is included to demonstrate the validit...

Adaptive discontinuous Galerkin approximations to fourth order parabolic problems

Abstract. An adaptive algorithm, based on residual type a posteriori indicators of errors measured in L∞(L2) and L2(L2) norms, for a numerical scheme consisting of implicit Euler method in time and discontinuous Galerkin method in space for linear parabolic fourth order problems is presented. The a posteriori analysis is performed for convex domains in two and three space dimensions for local s...

Difference Approximations to Partial Differential Equations

Unconditionally Explicit Stable Difference Schemes for Solving Some Linear and Non-Linear Parabolic Differential Equation

We present the numerical method for solution of some linear and non-linear parabolic equation. Using idea [1], we will present the explicit unconditional stable scheme which has no restriction on the step size ratio k/h2 where k and h are step sizes for space and time respectively. We will also present numerical results to justify the present scheme.