A computational study of the one-dimensional parabolic equation subject to nonclassical boundary specifications

Certain problems arising in engineering are modeled by nonstandard parabolic initial‐boundary value problems in one space variable, which involve an integral term over the spatial domain of a function of the desired solution. Hence, in the past few years interest has substantially increased in the s...

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Veröffentlicht in:	Numerical methods for partial differential equations Jg. 22; H. 1; S. 220 - 257
1. Verfasser:	Dehghan, Mehdi
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Hoboken Wiley Subscription Services, Inc., A Wiley Company 01.01.2006
Schlagworte:	boundary element method decomposition method double shifted Legendre series existence explicit schemes finite difference schemes Galerkin procedure implicit techniques Keller-box scheme Legendre Tau method nonstandard boundary value problems numerical integration orthogonal spline collocation pade approximant parallel algorithms product integration method representation of solutions Runge-Kutta-Chebyshev formula second-order parabolic equation semidiscretization techniques separation of variables stability uniqueness wavelet-Galerkin technique
ISSN:	0749-159X, 1098-2426
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Abstract	Certain problems arising in engineering are modeled by nonstandard parabolic initial‐boundary value problems in one space variable, which involve an integral term over the spatial domain of a function of the desired solution. Hence, in the past few years interest has substantially increased in the solutions of these problems. As a result numerous research papers have also been devoted to the subject. Although considerable amount of work has been done in the past, there is still a lack of a completely satisfactory computational scheme. Also, there are some cases that have not been studied numerically yet. In the current article several approaches for the numerical solution of the one‐dimensional parabolic equation subject to the specification of mass, which have been considered in the literature, are reported. Finite difference methods have been proposed for the numerical solution of the new nonclassic boundary value problem. To investigate the performance of the proposed algorithm, we consider solving a test problem. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006
AbstractList	Certain problems arising in engineering are modeled by nonstandard parabolic initial‐boundary value problems in one space variable, which involve an integral term over the spatial domain of a function of the desired solution. Hence, in the past few years interest has substantially increased in the solutions of these problems. As a result numerous research papers have also been devoted to the subject. Although considerable amount of work has been done in the past, there is still a lack of a completely satisfactory computational scheme. Also, there are some cases that have not been studied numerically yet. In the current article several approaches for the numerical solution of the one‐dimensional parabolic equation subject to the specification of mass, which have been considered in the literature, are reported. Finite difference methods have been proposed for the numerical solution of the new nonclassic boundary value problem. To investigate the performance of the proposed algorithm, we consider solving a test problem. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006
Author	Dehghan, Mehdi
Author_xml	– sequence: 1 givenname: Mehdi surname: Dehghan fullname: Dehghan, Mehdi email: mdehghan@aut.ac.ir organization: Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran
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Ionkin, Stability of a problem in heat transfer theory with a non-classical bounda 1995; 31 1993; 24 1974; 14 1982; 18 1973; 53 1991; 12 1999; 49 1984; 23 1964; 4 1995; 32 1992; 18 1999; 45 1994; 25 1983; 9 2005; 21 1999; 40 1998; 41 1985; 21 1996; 76 1992; 50 1985; 25 1993; 35 2002; 48 1989; VII 2000; 16 1984; 93 1978; 23 2002; 42 1986; 44 1993; 31 1963; 70 1987 1985 1988; 46 1999; 10 1970; 20 1982 1989; 79 1996; 2 1990; 130 1955; 13 1996; 9 1982; 130 1996; 6 1996; 67 1994; 32 1989 1988 1998; 27 1979; 16 1993; 47 1989; 5 1993; 107 2004; 149 1963; 21 2004; 81 2003; 80 1986; 115 1981; 1 1997; 20 2003; 2003 2002; 35 1991; 31 2000; 64 1992; 39 1999; 22 1997; 27 1994 1978; 15 1999; 106 1999; 5 1972; 2 1987; 24 1995; 190 1980; 16 1993; 13 1980; 15 2002; 26 1991; 27 1973; 20 1990; 28 1982; 40 1986; 22 1982; 86 1960; 27 1999; 110 1994; 13 1983; 41 1960 1977; 13 2003; 145 1994; 10 1992; 63 Lanczos C. (e_1_2_1_68_2) 1987 e_1_2_1_81_2 Allegretto W. (e_1_2_1_96_2) 1999; 5 e_1_2_1_89_2 Wang S. 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Snippet	Certain problems arising in engineering are modeled by nonstandard parabolic initial‐boundary value problems in one space variable, which involve an integral...
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SubjectTerms	boundary element method decomposition method double shifted Legendre series existence explicit schemes finite difference schemes Galerkin procedure implicit techniques Keller-box scheme Legendre Tau method nonstandard boundary value problems numerical integration orthogonal spline collocation pade approximant parallel algorithms product integration method representation of solutions Runge-Kutta-Chebyshev formula second-order parabolic equation semidiscretization techniques separation of variables stability uniqueness wavelet-Galerkin technique
Title	A computational study of the one-dimensional parabolic equation subject to nonclassical boundary specifications
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