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

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dc.contributor.author Hakeem, A
dc.contributor.author Rehman, S
dc.contributor.author Pervaiz, A
dc.contributor.author Iqbal, M.J
dc.date.accessioned 2022-10-26T10:04:02Z
dc.date.available 2022-10-26T10:04:02Z
dc.date.issued 2015-12-09
dc.identifier.citation Hakeem, A., Rehman, S., Pervaiz, A., & Iqbal, M. J. (2015). NON-POLYNOMIAL CUBIC SPLINE APPROACH FOR NUMERICAL APPROXIMATION OF SECOND ORDER LINEAR KLEIN-GORDON EQUATION. Pakistan Journal of Science, 67(4). en_US
dc.identifier.issn 2411-0930
dc.identifier.uri http://142.54.178.187:9060/xmlui/handle/123456789/13751
dc.description.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 en_US
dc.language.iso en en_US
dc.publisher Lahore:Pakistan Association for the Advancement of Science en_US
dc.subject Non-polynomial cubic spline technique en_US
dc.subject Finite difference approximations en_US
dc.subject System of partial differential equations en_US
dc.subject Second order linear Klein-Gordon equation en_US
dc.title NON-POLYNOMIAL CUBIC SPLINE APPROACH FOR NUMERICAL APPROXIMATION OF SECOND ORDER LINEAR KLEIN-GORDON EQUATION en_US
dc.type Article en_US


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