In this work,a numerical scheme is constructed for solving nonlinear parabolictype partial-integro differential equations.The proposed numerical scheme is based on radial basis functions which are local in nature like...In this work,a numerical scheme is constructed for solving nonlinear parabolictype partial-integro differential equations.The proposed numerical scheme is based on radial basis functions which are local in nature like finite difference numerical schemes.The radial basis functions are used to approximate the derivatives involved and the integral is approximated by equal width integration rule.The resultant differentiation matrices are sparse in nature.After spatial approximation using RBF the partial integro-differential equations reduce to the system of ODEs.Then ODEs system can be solved by various types of ODE solvers.The proposed numerical scheme is tested and compared with other methods available in literature for different test problems.The stability and convergence of the present numerical scheme are discussed.展开更多
In this paper a meshless method of lines is proposed for the numerical solution of time-dependent nonlinear coupled partial differential equations. Contrary to mesh oriented methods of lines using the finite-differenc...In this paper a meshless method of lines is proposed for the numerical solution of time-dependent nonlinear coupled partial differential equations. Contrary to mesh oriented methods of lines using the finite-difference and finite element methods to approximate spatial derivatives, this new technique does not require a mesh in the problem domain, and a set of scattered nodes provided by initial data is required for the solution of the problem using some radial basis functions. Accuracy of the method is assessed in terms of the error norms L2, L∞ and the three invariants C1, C2, C3. Numerical experiments are performed to demonstrate the accuracy and easy implementation of this method for the three classes of time-dependent nonlinear coupled partial differential equations.展开更多
In this paper,we approximate the solution and also discuss the periodic behavior termed as eventual periodicity of solutions of(IBVPs)for some dispersive wave equations on a bounded domain corresponding to periodic fo...In this paper,we approximate the solution and also discuss the periodic behavior termed as eventual periodicity of solutions of(IBVPs)for some dispersive wave equations on a bounded domain corresponding to periodic forcing.The constructed numerical scheme is based on radial kernels and local in nature like finite difference method.The temporal variable is executed through RK4 scheme.Due to the local nature and sparse differentiation matrices our numerical scheme efficiently recovers the solution.The results achieved are validated and examined with other methods accessible in the literature.展开更多
文摘In this work,a numerical scheme is constructed for solving nonlinear parabolictype partial-integro differential equations.The proposed numerical scheme is based on radial basis functions which are local in nature like finite difference numerical schemes.The radial basis functions are used to approximate the derivatives involved and the integral is approximated by equal width integration rule.The resultant differentiation matrices are sparse in nature.After spatial approximation using RBF the partial integro-differential equations reduce to the system of ODEs.Then ODEs system can be solved by various types of ODE solvers.The proposed numerical scheme is tested and compared with other methods available in literature for different test problems.The stability and convergence of the present numerical scheme are discussed.
文摘In this paper a meshless method of lines is proposed for the numerical solution of time-dependent nonlinear coupled partial differential equations. Contrary to mesh oriented methods of lines using the finite-difference and finite element methods to approximate spatial derivatives, this new technique does not require a mesh in the problem domain, and a set of scattered nodes provided by initial data is required for the solution of the problem using some radial basis functions. Accuracy of the method is assessed in terms of the error norms L2, L∞ and the three invariants C1, C2, C3. Numerical experiments are performed to demonstrate the accuracy and easy implementation of this method for the three classes of time-dependent nonlinear coupled partial differential equations.
文摘In this paper,we approximate the solution and also discuss the periodic behavior termed as eventual periodicity of solutions of(IBVPs)for some dispersive wave equations on a bounded domain corresponding to periodic forcing.The constructed numerical scheme is based on radial kernels and local in nature like finite difference method.The temporal variable is executed through RK4 scheme.Due to the local nature and sparse differentiation matrices our numerical scheme efficiently recovers the solution.The results achieved are validated and examined with other methods accessible in the literature.
