Title of article :
Second-order schemes for a boundary value problem with Neumannʹs boundary conditions
Author/Authors :
Dehghan، نويسنده , , Mehdi، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2002
Abstract :
A new second-order finite difference scheme based on the (3, 3) alternating direction implicit method and a new second-order finite difference technique based on the (5, 5) implicit formula are discussed for solving a nonlocal boundary value problem for the two-dimensional diffusion equation with Neumannʹs boundary conditions. While sharing some common features with the one-dimensional models, the solution of two-dimensional equations are substantially more difficult, thus some considerations are taken to be able to extend some ideas of the one-dimensional case. Using a suitable transformation the solution of this problem is equivalent to the solution of two other problems. The former, which is a one-dimensional nonlocal boundary value problem giving the value of μ through using the unconditionally stable standard implicit (3, 1) backward time-centred space (denoted BTCS) scheme. Using this result the second problem will be changed to a classical two-dimensional diffusion equation with Neumannʹs boundary conditions which will be solved numerically by using the unconditionally stable alternating direction implicit (3, 3) technique or the fully implicit finite difference scheme. The results of a numerical example are given and computation times are presented. Error estimates derived in the maximum norm are also tabulated.
Keywords :
Central processor time , Alternating Direction Implicit schemes , finite difference methods , Neumannיs boundary conditions , nonlocal boundary value problems , Parabolic partial differential equations , Two-dimensional heat equation , Implicit techniques
Journal title :
Journal of Computational and Applied Mathematics
Journal title :
Journal of Computational and Applied Mathematics