APPLICATION OF THIRD DERIVATIVE BLOCK METHODS FOR THE SOLUTION OF HYPERBOLIC PARTIAL DIFFERENTIAL EQUATIONS

Abstract

In this work, three scheme were developed, analyzed and applied to solve two dimensional hyperbolic Partial Di erential Equations (PDEs). The derivations were achieved by using collocation and interpolation techineques. The PDEs were converted to Ordinary Di erential Equations (ODEs) via method of lines by replacing the spartial derivatives with second-order central di erence formulas. The resulting system of ODEs were solved in a blockwise manner using the derived methods. Analysis of the derived methods revealed that they are zero-stable, consistent and convergent. The results obtained using the derived methods were compared with existing methods in the literature. It was observed that the derived methods compared favourably well with the existing methods.