NON-POLYNOMIAL CUBIC SPLINE APPROACH FOR NUMERICAL APPROXIMATION OF SECOND ORDER LINEAR KLEIN-GORDON EQUATION

Most of the fundamental theories and mathematical models engineering physical sciences are expressed in terms partial differential equations (PDEs). Several studies were carried out for numerical approximation second order linear Klein-Gordon equation. This study constructed a new technique The scheme was based on employing non-polynomial cubic spline method (NPCSM). time derivatives involved equation decomposed into first derivatives. decomposition generated system PDEs, where approximated by central finite differences . Three test problems considered illustration developed scheme. For different values spatial displacement , step size produced encouraging results which very much close to analytical solution. best observed accuracy machine precision.