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High order convergent modified nodal bi‐cubic spline collocation method for elliptic partial differential equation
Author(s) -
Singh Suruchi,
Singh Swarn
Publication year - 2020
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22463
Subject(s) - mathematics , superconvergence , elliptic partial differential equation , partial differential equation , dirichlet boundary condition , stencil , boundary value problem , collocation method , mathematical analysis , dirichlet problem , spline (mechanical) , collocation (remote sensing) , orthogonal collocation , elliptic curve , convergence (economics) , differential equation , finite element method , ordinary differential equation , physics , computational science , structural engineering , economic growth , engineering , economics , thermodynamics , remote sensing , geology
Abstract A high order modified nodal bi‐cubic spline collocation method is proposed for numerical solution of second‐order elliptic partial differential equation subject to Dirichlet boundary conditions. The approximation is defined on a square mesh stencil using nine grid points. The solution of the method exists and is unique. Convergence analysis has been presented. Moreover, the superconvergent phenomena can be seen in proposed one step method. The numerical results clearly exhibit the superiority of the new approximation, in terms of both accuracy and computational efficiency.