The numerical solution of fourth order mildly quasi-linear parabolic initial boundary value problem of second kind

In this article, we report on three-level implicit stable finite difference formulas of O(k ² + h ²) and O(k ² + h ⁴) for the numerical integration of certain mildly quasi-liner fourth order parabolic partial differential equations in one-space dimension. The numerical solution of u _xx is obtained as a by-product of the method. In all cases, we use only (3 + 3 + 3)-grid points and a single computational cell. Difference schemes for the fourth order linear parabolic equation in polar coordinates are also discussed. The stability analysis for the model linear problem is given as a representative example. Numerical results are presented to demonstrate the order and accuracy of the proposed methods.

Keywords:

• Fourth Order Quasi-linear Parabolic Equation
• Implicit Scheme
• Polar Coordinates
• Second Order Derivative
• Rms Errors