Higher order B‐spline differential quadrature rule to approximate generalized Rosenau‐RLW equation
In this article, B‐spline‐based collocation method is employed to approximate the usual and modified Rosenau‐RLW nonlinear equations. The weighted extended B‐spline (WEB‐spline) is used as the modified form of B‐spline as the usual B‐splines fail to obey the Dirichlet boundary conditions. The WEB me...
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| Veröffentlicht in: | Mathematical methods in the applied sciences 2020-07, Vol.43 (11), p.6812-6822 |
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| container_title | Mathematical methods in the applied sciences |
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| creator | Mustahsan, Muhammad Kiran, Ayesha Singh, Jagdev Nisar, Kottakkaran Sooppy Kumar, Devendra |
| description | In this article, B‐spline‐based collocation method is employed to approximate the usual and modified Rosenau‐RLW nonlinear equations. The weighted extended B‐spline (WEB‐spline) is used as the modified form of B‐spline as the usual B‐splines fail to obey the Dirichlet boundary conditions. The WEB method is more general method that allows to discretize the domain into finite number of elements not necessarily start from the boundary points of the domain. Our method omits the linearization process of the nonlinear partial differential equation (PDE). Different cases are discussed by setting the parameter p=2,3,4, and 6 that appears in Rosenau‐RLW equations. The error estimation is calculated, which gives good agreement of the exact solution. |
| doi_str_mv | 10.1002/mma.6423 |
| format | Article |
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| subjects | Boundary conditions collocation method Collocation methods Dirichlet problem Domains Exact solutions Mathematical analysis Nonlinear differential equations Nonlinear equations Partial differential equations Quadratures Rosenau‐RLW equation SSP‐RK54 scheme Thomas algorithm Webs WEB‐spline |
| title | Higher order B‐spline differential quadrature rule to approximate generalized Rosenau‐RLW equation |
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