The use of Chebyshev cardinal functions for the solution of a partial differential equation with an unknown time-dependent coefficient subject to an extra measurement

• Published in: Journal of computational and applied mathematics Vol. 235; no. 3; pp. 669 - 678
• Main Authors: Lakestani, Mehrdad, Dehghan, Mehdi
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier B.V 01.12.2010; Elsevier
• Subjects: Algebra; Approximation; Chebyshev approximation; Chebyshev cardinal functions; Coefficients; Computation; Derivatives; Exact sciences and technology; Mathematical analysis; Mathematical models; Mathematics; Numerical analysis; Numerical analysis in abstract spaces; Numerical analysis. Scientific computation; Operational matrix of derivative; Parabolic inverse problem; Parameter determination 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; Unknown diffusion coefficient; Operational matrix of derivative; Parabolic inverse problem; Parameter determination problem; Chebyshev cardinal functions; Unknown diffusion coefficient; Initial value problem; Partial differential equation; Inverse problem; Parabolic equation; Numerical analysis; Boundary value problem; Applied mathematics; Algebraic equation
• ISSN: 0377-0427; 1879-1778
• DOI: 10.1016/j.cam.2010.06.020

A numerical technique is presented for the solution of a parabolic partial differential equation with a time-dependent coefficient subject to an extra measurement. The method is derived by expanding the required approximate solution as the elements of Chebyshev cardinal functions. Using the operational matrix of derivative, the problem can be reduced to a set of algebraic equations. From the computational point of view, the solution obtained by this method is in excellent agreement with those obtained by previous works and also it is efficient to use.