Recent Developments on Operator-Difference Schemes for Solving Nonlocal BVPs for the Wave Equation | Zendy

Mehmet Emir Köksal | Zendy

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Recent Developments on Operator-Difference Schemes for Solving Nonlocal BVPs for the Wave Equation

Author(s) -

Mehmet Emir Köksal

Publication year - 2011

Publication title -

discrete dynamics in nature and society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.264

H-Index - 39

eISSN - 1607-887X

pISSN - 1026-0226

DOI - 10.1155/2011/210261

Subject(s) - operator (biology) , mathematics , hyperbolic partial differential equation , cauchy distribution , variable (mathematics) , partial differential equation , scheme (mathematics) , mathematical analysis , boundary (topology) , order (exchange) , boundary value problem , space (punctuation) , ftcs scheme , differential equation , computer science , ordinary differential equation , biochemistry , chemistry , finance , repressor , transcription factor , economics , gene , differential algebraic equation , operating system

The second-order one-dimensional linear hyperbolic equation with time and space variable coefficients and nonlocal boundary conditions is solved by using stable operator-difference schemes. Two new second-order difference schemes recently appeared in the literature are compared numerically with each other and with the rather old first-order difference scheme all to solve abstract Cauchy problem for hyperbolic partial differential equations with time-dependent unbounded operator coefficient. These schemes are shown to be absolutely stable, and the numerical results are presented to compare the accuracy and the execution times. It is naturally seen that the second-order difference schemes are much more advantages than the first-order ones. Although one of the second-order difference scheme is less preferable than the other one according to CPU (central processing unit) time consideration, it has superiority when the accuracy weighs more importance

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