TY - JOUR
TI - Non-polynomial cubic spline method used to fathom Sine Gordon equations in 3+1 dimensions
AU - Sattar Rabia
AU - Ahmad Muhammad Ozair
AU - Pervaiz Anjum
AU - Ahmed Nauman
AU - Akgül Ali
AU - Abdullaev Sherzod
AU - Alshaikh Noorhan
AU - Wannan Rania
AU - Asad Jihad
JN - Thermal Science
PY - 2023
VL - 27
IS - 4
SP - 3155
EP - 3170
PT - Article
AB - This study contains an algorithmic solution of the Sine Gordon equation in  three space and time dimensional problems. For discretization, the central  difference formula is used for the time variable. In contrast, space  variable x, y, and z are discretized using the non-polynominal cubic spline  functions for each. The proposed scheme brings the accuracy of order O(h2 +  k2 + σ2 + τ2h2 + τ2k2 + τ2σ2) by electing suitable parametric values. The  paper also discussed the truncation error of the proposed method and  obtained the stability analysis. Numerical problems are elucidated by this  method and compared to results taken from the literature.