The Extrapolated Crank–Nicolson Orthogonal Spline Collocation Method for a Quasilinear Parabolic Problem with Nonlocal Boundary Conditions

2014 ◽  
Vol 62 (1) ◽  
pp. 265-283 ◽  
Author(s):  
B. Bialecki ◽  
G. Fairweather ◽  
J. C. López-Marcos
Keyword(s):  
Boundary Conditions ◽  
Collocation Method ◽  
Parabolic Problem ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Spline Collocation ◽  
Spline Collocation Method ◽  
Orthogonal Spline Collocation ◽  
Quasilinear Parabolic Problem ◽  
Quasilinear Parabolic

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

2013 ◽  
Vol 5 (04) ◽  
pp. 442-460 ◽  
Author(s):  
B. Bialecki ◽  
G. Fairweather ◽  
J.C. López-Marcos
Keyword(s):  
Boundary Conditions ◽  
Heat Equation ◽  
Collocation Method ◽  
Error Estimates ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Maximum Norm ◽  
Spline Collocation ◽  
Spline Collocation Method ◽  
Orthogonal Spline Collocation

AbstractWe 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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