Two-dimensional Differential Transform Method for Solving Linear and Non-linear Goursat Problem

A method for solving linear and non-linear Goursat problem is given by using the two-dimensional differential transform method. The approximate solution of this problem is calculated in the form of a series with easily computable terms and also the exact solutions can be achieved by the known forms of the series solutions. The method can easily be applied to many linear and non-linear problems and is capable of reducing the size of computational work. Several examples are given to demonstrate the reliability and the performance of the presented method.

Authors:

• H. Taghvafard
• G. H. Erjaee

Keywords:

• Quadrature
• Spline interpolation
• Trapezoidal rule
• Numericalintegration
• Error analysis.

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