Smoothing of Crank–Nicolson scheme for the two-dimensional diffusion with an integral condition

• Published in: Applied mathematics and computation Vol. 214; no. 2; pp. 512 - 522
• Main Author: Siddique, Mohammad
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Inc 15.08.2009; Elsevier
• Subjects: Crank–Nicolson Scheme; Exact sciences and technology; Mathematical analysis; Mathematics; Nonlocal boundary conditions; Numerical analysis; Numerical analysis. Scientific computation; Numerical approximation; Partial differential equations; Partial differential equations, boundary value problems; Partial differential equations, initial value problems and time-dependant initial-boundary value problems; Sciences and techniques of general use; Smoothing; Two-dimensional parabolic problems; Nonlocal boundary conditions; Crank–Nicolson Scheme; Smoothing; Two-dimensional parabolic problems; Matrix approximation; Smoothing methods; Process control; Initial value problem; Numerical method; Boundary condition; Partial differential equation; Crank-Nicolson Scheme; Numerical approximation; Parabolic equation; Numerical analysis; Boundary value problem; Applied mathematics; Diffusion process; Two-dimensional calculations; Padé approximant; Control theory; Padé approximation
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2009.04.025

The Parabolic partial differential equations (PDEs) with nonlocal boundary conditions model various physical phenomena, e.g. chemical diffusion, thermoelasticity, heat conduction process, control theory and medicine science. This paper deals with the smoothing of the Crank–Nicolson numerical scheme for two-dimensional parabolic PDEs with nonlocal boundary conditions. We use the numerical scheme based on Padé approximations of the matrix exponential. The graphs of numerical results demonstrate the successful smoothing of the Crank–Nicolson numerical scheme.