New algorithm for solving a nonlinear hyperbolic telegraph equation with an integral condition

International Journal for Numerical Methods in Biomedical Engineering

Volumn 27, Issue 10, 2011, Pages 1558-1568

  Yao, Huanmin ^a   Lin, Yingzhen ^b  

^a HARBIN NORMAL UNIVERSITY   (China)

^b HARBIN INSTITUTE OF TECHNOLOGY   (China)

Author keywords

Integral conditions; Nonlinear hyperbolic telegraph equation; Reproducing kernel space

Indexed keywords

EXACT SOLUTION; INTEGRAL CONDITIONS; NONLINEAR HYPERBOLIC TELEGRAPH EQUATION; REPRODUCING KERNEL SPACE; TELEGRAPH EQUATION;

TELEGRAPH;

NONLINEAR EQUATIONS;

EID: 80053240461     PISSN: 20407939     EISSN: 20407947     Source Type: Journal    
DOI: 10.1002/cnm.1376     Document Type: Article

References (23)

1. Bouziani A, Merazga N. Solution to a semilinear pseudoparabolic problem with integral conditions. Electronic Journal of Differential Equations 2006; 115:1-18.
2. Merazga N, Bouziani A. On a time-discretization method for a semilinear heat equation with purely integral conditions in a nonclassical function space. Nonlinear Analysis 2007; 66:604-623.
3. Pulkina LS. A non-local problem with integral conditions for hyperbolic equations. Electronic Journal of Differential Equations 1999; 45:1-6.
4. Bahuguna D, Shukla RK. Partial functional differential equations and applications to population dynamics. Nonlinear Dynamics and Systems Theory 2005; 5(4):345-356.
5. Nakhushev AM. On certain approximate method for boundary-value problems for differential equations and its applications in ground waters dynamics. Differentsialnie Uravnenia 1982; 18:72-81.
6. Ramezani M, Dehghan M, Razzaghi M. Combined finite difference and spectral methods for the numerical solution of hyperbolic equation with an integral condition. Numerical Methods for Partial Differential Equations 2008; 24:1-8.
7. Dehghan M, Lakestani M. 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 2007; 23:1277-1289.
8. Saadatmandi A, Dehghan M. Numerical solution of the one-dimensional wave equation with an integral condition Inc. Numerical Methods for Partial Differential Equations 2007; 23:282-292.
9. Dehghan M. On the solution of an initial-boundary value problem that combines Neumann and integral condition for the wave equation. Numerical Methods for Partial Differential Equations 2005; 21:24-40.
10. Shakeri F, Dehghan M. The method of lines for solution of the one-dimensional wave equation subject to an integral conservation condition. Computers and Mathematics with Applications 2008; 56:2175-2188.
11. Guezane-Lakouda A, Belakroumb D. Rothe's method for a telegraph equation with integral conditions. Nonlinear Analysis 2009; 70:3842-3853.
12. Cui MG, Chen Z. The exact solution of nonlinear age-structured population model. Nonlinear Analysis: Real World Applications 2007; 8:1096-1112.
13. Capobianco E. Kernel methods and flexible inference for complex stochastic dynamics. Physica A: Statistical Mechanics and its Applications 2008; 387:4077-4098.
14. Zhou YF, Lin YZ, Cui MG. An efficient computational method for second order boundary value problems of nonlinear differential equations. Applied Mathematics and Computation 2007; 194:354-365.
15. Geng FZ, Cui MG. Solving singular nonlinear second-order periodic boundary value problems in the reproducing kernel space. Applied Mathematics and Computation 2007; 192:389-398.
16. Cui MG, Geng FZ. Solving singular two-point boundary value problem in reproducing kernel space. Journal of Computational and Applied Mathematics 2007; 205:6-15.
17. Geng FZ, Cui MG. A computational method for solving one-dimensional variable-coefficient Burgers equation. Applied Mathematics and Computation 2007; 188:1389-1401.
18. Dehghan M, Shokri A. A numerical method for solving the hyperbolic telegraph equation. Numerical Methods for Partial Differential Equations 2008; 24:1080-1093.
19. Dehghan M, Lakestani M. The use of Chebyshev cardinal functions for solution of the second-order one-dimensional telegraph equation. Numerical Methods for Partial Differential Equations 2009; 25:931-938.
20. Saadatmandi A, Dehghan M. Numerical solution of hyperbolic telegraph equation using the Chebyshev tau method. Numerical Methods for Partial Differential Equations 2010; 26(1):239-252.
21. Yousefi SA. Legendre multiwavelet Galerkin method for solving the hyperbolic telegraph equation. Numerical Methods for Partial Differential Equations 2009; DOI: 10.1002/num.20445.
22. Cui MG, Lin YZ. Nonlinear Numerical Analysis in the Reproducing Kernel Space. Nova Science Publisher: New York, 2008.
23. Aronszajn N. Theory of reproducing kernel. Transactions of the American Mathematical Society 1950; 168:1-50.