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