Geometric Mesh Three-Point Discretization for Fourth-Order Nonlinear Singular Differential Equations in Polar System | Zendy

Navnit Jha | Zendy; R. K. Mohanty | Zendy; Vinod Kumar Chauhan | Zendy

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Geometric Mesh Three-Point Discretization for Fourth-Order Nonlinear Singular Differential Equations in Polar System

Author(s) -

Navnit Jha,

R. K. Mohanty,

Vinod Kumar Chauhan

Publication year - 2013

Publication title -

advances in numerical analysis

Language(s) - English

Resource type - Journals

eISSN - 1687-9570

pISSN - 1687-9562

DOI - 10.1155/2013/614508

Subject(s) - mathematics , discretization , tridiagonal matrix , nonlinear system , convergence (economics) , mathematical analysis , order of accuracy , backward differentiation formula , numerical analysis , differential equation , ordinary differential equation , numerical partial differential equations , differential algebraic equation , eigenvalues and eigenvectors , physics , quantum mechanics , economics , economic growth

Numerical method based on three geometric stencils has been proposed for the numerical solution of nonlinear singular fourth-order ordinary differential equations. The method can be easily extended to the sixth-order differential equations. Convergence analysis proves the third-order convergence of the proposed scheme. The resulting difference equations lead to block tridiagonal matrices and can be easily solved using block Gauss-Seidel algorithm. The computational results are provided to justify the usefulness and reliability of the proposed method

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