zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
A tau method for the one-dimensional parabolic inverse problem subject to temperature overspecification. (English) Zbl 1125.65340
Summary: An approximational technique based on shifted Legendre-tau ideas is presented for the one-dimensional parabolic inverse problem with a control parameter. The method consists of expanding the required approximate solution as the elements of a shifted Legendre polynomial. Using the operational matrices we reduce the problem to a set of algebraic equations. A numerical example is included to demonstrate the validity and applicability of the technique and a comparison is made with existing results. The method is easy to implement and produces very accurate results.

65M32Inverse problems (IVP of PDE, numerical methods)
65M70Spectral, collocation and related methods (IVP of PDE)
35R30Inverse problems for PDE
35K15Second order parabolic equations, initial value problems
Full Text: DOI
[1] Lanczos, C.: Applied analysis. (1956) · Zbl 0111.12403
[2] Kalla, S. L.; Khajah, H. G.: Tau method approximation of the hubbell rectangular source integral. Radiat. phys. Chem. 59, No. 1, 17-21 (2000)
[3] Razzaghi, M.; Oppenheimer, S.; Ahmad, F.: Tau method approximation for radiative transfer problems in a slab medium. J. quantitative spectrosc. Radia. transfer 72, No. 4, 439-447 (2002)
[4] Saadatmandi, A.; Razzaghi, M.: A tau method approximation for the diffusion equation with nonlocal boundary conditions. International journal of computer mathematics 81, 1427-1432 (2004) · Zbl 1063.65110
[5] Canuto, C.; Hussaini, M. Y.; Quarteroni, A.; Zang, T. A.: Spectral methods in fluid dynamic. (1988) · Zbl 0658.76001
[6] Cannon, J. R.; Lin, Y.; Xu, S.: Numerical procedures for the determination of an unknown coefficient in semi-linear parabolic differential equations. Inverse problems 10, 227-243 (1994) · Zbl 0805.65133
[7] Cannon, J. R.; Yin, H. M.: Numerical solutions of some parabolic inverse problems. Numerical methods for partial differential equations 2, 177-191 (1990) · Zbl 0709.65105
[8] Cannon, J. R.; Lin, Y.: An inverse problem of finding a parameter in a semi-linear heat equation. J. math. Anal. appl. 145, No. 2, 470-484 (1990) · Zbl 0727.35137
[9] Cannon, J. R.; Yin, H. M.: On a class of non-classical parabolic problems. J. differential equations 79, No. 2, 266-288 (1989) · Zbl 0702.35120
[10] Cannon, J. R.; Lin, Y.; Wang, S.: Determination of source parameter in parabolic equations. Meccanica 27, 85-94 (1992) · Zbl 0767.35105
[11] Cannon, J. R.; Yin, H. M.: On a class of nonlinear parabolic equations with nonlinear trace type functionals inverse problems. Inverse problems 7, 149-161 (1991) · Zbl 0735.35078
[12] Dehghan, M.: An inverse problem of finding a source parameter in a semilinear parabolic equation. Applied mathematical modelling 25, 743-754 (2001) · Zbl 0995.65098
[13] Dehghan, M.: Fourth-order techniques for identifying a control parameter in the parabolic equations. International journal of engineering science 40, 433-447 (2002) · Zbl 1211.65120
[14] Dehghan, M.: Numerical solution of one-dimensional parabolic inverse problem. Applied mathematics and computation 136, 333-344 (2003) · Zbl 1026.65078
[15] Dehghan, M.: Efficient techniques for the second-order parabolic equation subject to nonlocal specifications. Applied numerical mathematics 52, No. 1, 39-62 (2005) · Zbl 1063.65079
[16] Dehghan, M.: Parameter determination in a partial differential equation from the overspecified data. Mathl. comput. Modelling 41, No. 2/3, 197-213 (2005) · Zbl 1080.35174
[17] Lin, Y.; Tait, R. J.: On a class of non-local parabolic boundary value problems. International journal of engineering science 32, No. 3, 395-407 (1994) · Zbl 0792.73018
[18] Wang, S.: Numerical solutions of two inverse problems for identifying control parameters in 2-dimensional parabolic partial differential equations. Htp 194, 11-16 (1992)
[19] Wang, S.; Lin, Y.: A finite difference solution to an inverse problem determining a control function in a parabolic partial differential equation. Inverse problems 5, 631-640 (1989) · Zbl 0683.65106
[20] Gottlieb, D.; Hussaini, M.; Orszag, S.: Theory and applications of spectral methods. Spectral methods for partial differential equations (1984) · Zbl 0599.65079