The use of cubic B-spline scaling functions for solving the one-dimensional hyperbolic equation with a nonlocal conservation condition

Numerical Methods for Partial Differential Equations

Volumn 23, Issue 6, 2007, Pages 1277-1289

  Dehghan, Mehdi ^a   Lakestani, Mehrdad ^b  

^a AMIRKABIR UNIVERSITY OF TECHNOLOGY   (Iran)

^b UNIVERSITY OF TABRIZ   (Iran)

Author keywords

Cubic B spline scaling functions; Nonclassic boundary condition; Wave equation

Indexed keywords

EID: 35948976970     PISSN: 0749159X     EISSN: 10982426     Source Type: Journal    
DOI: 10.1002/num.20209     Document Type: Article

References (36)

1. 1 B. A. Boley and J. H. Weiner, Theory of thermal stresses, Wiley, New York, 1960.
2. 2 A. Bouziani, Strong solution for a mixed problem with nonlocal condition for certain pluriparabolic equations, Hiroshima Math J 27 (3) ( 1997), 373–390.
3. 3 A. Bouziani, Mixed problem with boundary integral conditions for a certain parabolic equation, J Appl Math Stochastic Anal 9 (3) ( 1996), 323–330.
4. 4 A. Bouziani, On a third order parabolic equation with a nonlocal boundary condition, J Appl Math Stochastic Anal 13 (2) ( 2000), 181–195.
5. 5 Y. S. Choi and K. Y. Chan, A parabolic equation with nonlocal boundary conditions arising from electrochemistry, Nonlinear Anal Theor Methods Appl 18 (4) ( 1992), 317–331.
6. 6 I. S. Gordeziani and G. A. Avalishvili, On the constructing of solutions of the nonlocal initial boundary problems for one‐dimensional medium oscillation equations, Matem Modelirovanie 12 (1) ( 2000), 94–103.
7. 7 B. Jumarhon and S. McKee, On a heat equation with nonlinear and nonlocal boundary conditions, J Math Anal Appl 190 ( 1995), 806–820.
8. 8 S. Mesloub and A. Bouziani, On a class of singular hyperbolic equation with a weighted integral condition, Int J Math Math Sci 22 (3) ( 1999), 511–519.
9. 9 L. A. Muravei and A. V. Philinovskii, Non‐local boundary value problems for hyperbolic equation, Matem Zametki 54 ( 1993), 98–116.
10. 10 L. S. Pulkina, A nonlocal problem with integral conditions for hyperbolic equations, Electr J Differential Eq 45 ( 1999), 1–6.
11. 11 L. S. Pulkina, On solvability in L 2 of nonlocal problem with integral conditions for hyperbolic equations, Differets Uravn 2 ( 2000), 1–6.
12. 12 M. Renardy, W. Hrusa, and J. A. Nohel, Mathematical problems in viscoelasticity, Longman Science and Technology, England, 1987.
13. 13 V. V. Shelukhin, A non‐local in time model for radionuclides propagation in Stokes fluids, dynamics of fluids with free boundaries, Siberian Russian Acad Sci Inst Hydrodynam 107 ( 1993), 180–193.
14. 14 A. Bouziani, Initial‐boundary value problem with a nonlocal condition for a viscosity equation, Int J Math Math Sci 30 (6) ( 2002), 327–338.
15. 15 S. Mesloub and A. Bouziani, Mixed problems with integral conditions for a certain class of hyperbolic equations, J Appl Math 1 (30) ( 2001), 107–116.
16. 16 S. A. Beilin, Existence of solutions for one‐dimensional wave equations with nonlocal conditions, Electr J Differential Eq 76 ( 2001), 1–8.
17. 17 W. T. Ang, A method of solution for the one‐dimensional heat equation subject to a nonlocal condition, SEA Bull Math 26 (2) ( 2002), 197–203.
18. 18 M. Dehghan, Efficient techniques for the second‐order parabolic equation subject to nonlocal specifications, Appl Numer Math 52 (1) ( 2005), 39–62.
19. 19 M. Dehghan, Saulyev's techniques for solving a parabolic equation with a non linear boundary specification, Int J Comput Math 80 (2) ( 2003), 257–265.
20. 20 M. Dehghan, Numerical solution of a non‐local boundary value problem with Neumann's boundary conditions, Commun Numer Methods Eng 19 (1) ( 2003), 1–12.
21. 21 M. Dehghan, Numerical solution of a parabolic equation subject to specification of energy, Appl Math Comput 149 (1) ( 2004), 31–45.
22. 22 Y. Lin, Parabolic partial differential equations subject to non‐local boundary conditions, Ph.D. dissertation, Department of Pure and Applied Mathematics, Washington State University, 1988.
23. 23 M. Dehghan, On the solution of an initial‐boundary value problem that combines Neumann and integral condition for the wave equation, Numer Methods Partial Differential Eq 21 ( 2005), 24–40.
24. 24 W. T. Ang, A numerical method for the wave equation subject to a non‐local conservation condition, Appl Numer Math 56 (8) ( 2006), 1054–1060.
25. 25 A. Guido, M. L. Di Silvestre, E. Francomano, and A. Tortorici, An advanced numerical model in solving thin‐wire integral equations by using semiorthogonal compactly supported spline wavelets, IEEE Trans Electromagnetic Compatibility 45 (2) ( 2003), 218–228.
26. 26 R. D. Nevels, J. C. Goswami, and H. Tehrani, Semiorthogonal wavelets basis sets for solving integral equations, IEEE Trans Antennas Propagations 45 ( 1997), 1332–1339.
27. 27 C. K. Chui, An introduction to wavelets, Academic, Boston, 1992.
28. 28 J. R. Cannon, The one dimensional heat equation, Encyclopedia of mathematics and its applications, Vol. 23, Addison‐Welsey, Menlo Park, CA, 1984.
29. 29 G. Dagan, The significance of heterogeneity of evolving scales to transport in porous formations, Water Res Res 13 ( 1994), 3327–3336.
30. 30 M. Dehghan, Numerical solution of a parabolic equation with non‐local boundary specifications, Appl Math Comput 145 ( 2003), 185–194.
31. 31 L. Lapidus and G. F. Pinder, Numerical solution of partial differential equations in science and engineering, John Wiley, New York, 1982.
32. 32 A. M. Nakhushev, On certain approximate methods for boundary‐value problems for differntial equations and its applications in ground waters dynamics, Differentsialnie Uravneinia 18 ( 1982), 72–81.
33. 33 M. Dehghan, Solution of a partial integro‐differential equation arising from viscoelasticity, International Journal of Computer Mathematics 83 (1) ( 2006), 123–129.
34. 34 M. Dehghan, The one‐dimensional heat equation subject to a boundary integral specification, Chaos, Solitons and Fractals 32 ( 2007), 661–675.
35. 35 M. Dehghan, A computational study of the one‐dimensional parabolic equation subject to nonclassical boundary specifications, Numer Methods Partial Differ Equations 22 ( 2006), 220–257.
36. 36 M. Dehghan, Finite difference procedures for solving a problem arising in modeling and design of certain optoelectronic devices, Mathematics and Computers in Simulation 71 ( 2006), 16–30.