Algorithmic solution for (3+1) Dimensional Klein-Gordon Equation using Non-Polynomial Cubic Spline Technique

Abstract

The algorithmic solution of problems based on the Klein-Gordon Equation in (3+1) dimensions has been discussed in this study. Time variable t is discretized by using the central difference formula. Cubic Spline function involving trigonometric functions is used for all three spacial variables and Suitable parametric values provide the accuracy of order O(h^2+k^2+σ^2+τ^2 h^2+τ^2 k^2+τ^2 σ^2 ) in our proposed scheme. The stability of this scheme is also discussed in this paper and the truncation error too. This method elucidates numerical problems and compares them to the results obtained from the literature.