A numerical solution for non-classical parabolic problem based on Chebyshev spectral collocation method

• Published in: Applied mathematics and computation Vol. 190; no. 1; pp. 179 - 185
• Main Authors: Golbabai, A., Javidi, M.
• Format: Journal Article
• Language: English
• Published: New York, NY Elsevier Inc 01.07.2007; Elsevier
• Subjects: Chebyshev polynomials; Exact sciences and technology; Global analysis, analysis on manifolds; Local interpolating functions; Mathematical analysis; Mathematics; Non-classical conditions; Numerical analysis; Numerical analysis. Scientific computation; Parabolic problem; 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; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds; Local interpolating functions; Parabolic problem; Chebyshev polynomials; Non-classical conditions; Chebyshev polynomial; Initial value problem; Numerical method; Polynomial method; Partial differential equation; Parabolic equation; Numerical analysis; Boundary value problem; Applied mathematics; Numerical solution; Collocation method
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2007.01.033

A numerical method based on Chebyshev polynomials and local interpolating functions is proposed for solving the one-dimensional parabolic partial differential equation subject to non-classical conditions. To assess its validity and accuracy, the method is applied to solve several test problem.