Method of lines solutions of the parabolic inverse problem with an overspecification at a point

• Published in: Numerical algorithms Vol. 50; no. 4; pp. 417 - 437
• Main Authors: Dehghan, Mehdi, Shakeri, Fatemeh
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01.04.2009; Springer Nature B.V
• Subjects: Algebra; Algorithms; Approximation; Boundary value problems; Computer Science; Derivatives; Differential equations; Finite difference method; Inverse problems; Mathematical analysis; Mathematical models; Method of lines; Numeric Computing; Numerical Analysis; Original Paper; Overspecification; Theory of Computation; Overspecified boundary data; Method of lines (MOL); Control parameter; System of ordinary differential equations (ODEs); Parabolic partial differential equations; Inverse problem
• ISSN: 1017-1398; 1572-9265
• DOI: 10.1007/s11075-008-9234-3

The present work is motivated by the desire to obtain numerical solution to a quasilinear parabolic inverse problem. The solution is presented by means of the method of lines. Method of lines is an alternative computational approach which involves making an approximation to the space derivatives and reducing the problem to a system of ordinary differential equations in the variable time, then a proper initial value problem solver can be used to solve this ordinary differential equations system. Some numerical examples and also comparison with finite difference methods will be investigated to confirm the efficiency of this procedure.