Computation of Non-Linear Fourth-Order Partial Differential Equation Using a Modified Second Order Fully Implicit Difference Scheme

Abstract: In the work reported herein, a second order accurate difference scheme is formulated and analyzed for fourth order nonlinear differential equations. Encouraging conclusions are obtained for the error and accompanying error norms. Computed simulations are compared with those in the literature and are found to not only corroborate theory and accuracy, but also justify the applicability of the scheme in more rigorous settings involving nonlinearity and higher order differential equations.