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The Crank-Nicolson Hermite Cubic Orthogonal Spline Collocation Method for the Heat Equation with Nonlocal Boundary Conditions

The Crank-Nicolson Hermite Cubic Orthogonal Spline Collocation Method for the Heat Equation with Nonlocal Boundary Conditions
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Year:    2013

Author:    B. Bialecki, G. Fairweather, J. C. Lόpez-Marcos

Advances in Applied Mathematics and Mechanics, Vol. 5 (2013), Iss. 4 : pp. 442–460

Abstract

We formulate and analyze the Crank-Nicolson Hermite cubic orthogonal spline collocation method for the solution of the heat equation in one space variable with nonlocal boundary conditions involving integrals of the unknown solution over the spatial interval. Using an extension of the analysis of Douglas and Dupont [23] for Dirichlet boundary conditions, we derive optimal order error estimates in the discrete maximum norm in time and the continuous maximum norm in space. We discuss the solution of the linear system arising at each time level via the capacitance matrix technique and the package COLROW for solving almost block diagonal linear systems. We present numerical examples that confirm the theoretical global error estimates and exhibit superconvergence phenomena.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.13-13S03

Advances in Applied Mathematics and Mechanics, Vol. 5 (2013), Iss. 4 : pp. 442–460

Published online:    2013-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    19

Keywords:    Heat equation nonlocal boundary conditions orthogonal spline collocation Hermite cubic splines convergence analysis superconvergence.

Author Details

B. Bialecki

G. Fairweather

J. C. Lόpez-Marcos

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