Application of 2D-BPFs to nonlinear integral equations

Communications in Nonlinear Science and Numerical Simulation

Volumn 15, Issue 3, 2010, Pages 527-535

  Maleknejad, K ^a   Sohrabi, S ^b   Baranji, B ^b  

^a ISLAMIC AZAD UNIVERSITY   (Iran)

^b IRAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Iran)

Author keywords

First kind integral equations; Nonlinear equations; Operational matrix; Two dimensional block pulse functions; Two dimensional Volterra integral equations

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; INTEGRAL EQUATIONS;

FIRST KIND INTEGRAL EQUATIONS; NONLINEAR INTEGRAL EQUATIONS; OPERATIONAL MATRICES; OPERATIONAL MATRIX OF INTEGRATION; PIECE-WISE CONSTANTS; TRIANGULAR SYSTEM; TWO-DIMENSIONAL; TWO-DIMENSIONAL BLOCK PULSE FUNCTIONS; TWO-DIMENSIONAL VOLTERRUM INTEGRAL EQUATION; VOLTERRA INTEGRAL EQUATIONS;

NONLINEAR EQUATIONS;

EID: 70349979715     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2009.04.011     Document Type: Article

References (16)

1. Mckee S., Tang T., and Diogo T. An Euler-type method for two-dimensional Volterra integral equations of the first kind. IMA J Numer Anal 20 (2000) 423-440
2. Hanson R., and Phillips J. Numerical solution of two-dimensional integral equations using linear elements. SIAM J Numer Anal 15 (1978) 113-121
3. Tikhonov A.N., and Arsenin V.Y. Solutions of ill-posed problems (1977), Winston, Washington, DC
4. Babolian E., and Masouri Z. Direct method to solve Volterra integral equation of the first kind using operational matrix with block-pulse functions. J Comput Appl Math 220 1, 2 (2008) 51-57
5. Bel'tyukov B.A., and Kuznechikhina L.N. A Rung-Kutta method for the solution of two-dimensional nonlinear Volterra integral equations. Differential Equations 12 (1976) 1163-1173
6. Singh P. A note on the solution of two-dimensional Volterra integral equations by spline. Indian J Math 18 (1979) 61-64
7. Brunner H., and Kauthen J.P. The numerical solution of two-dimensional Volterra integral equations by collocation and iterated collocation. IMA J Numer Anal 9 (1989) 47-59
8. Han G.Q., and Zhang L.Q. Asymptotic error expansion of two-dimensional Volterra integral equation by iterated collocation. Appl Math Comput 61 (1994) 269-285
9. Guoqiang H., Hayami K., Sugihara K., and Jiong W. Extrapolation method of iterated collocation solution for two-dimensional non-linear Volterra integral equation. Appl Math Comput 112 (2000) 49-61
10. Hadizadeh M., and Moatamedi N. A new differential transformation approach for two-dimensional Volterra integral equations. Int J Comp Math 84 (2007) 515-529
11. Xie W.-J., and Lin F.-R. A fast numerical solution method for two-dimensional Fredholm integral equations of the second kind. Appl Numer Math (2009) 10.1016/j.apnum.2009.01.009
12. Rao G.P. Piecewise constant orthogonal functions and their application to systems and control (1983), Springer-Verlag, New York
13. Jiang Z.H., and Schaufelberger W. Block pulse functions and their applications in control systems (1992), Springer-Verlag, Berlin
14. Wang C.H., and Shih Y.P. Explicit solutions of integral equations via block-pulse functions. Int J Syst Sci 13 (1982) 773-782
15. Maleknejad K., Shahrezaee M., and Khatami H. Numerical solution of integral equations system of the second kind by Block-Pulse functions. Appl Math Comput 166 (2005) 15-24
16. Rudin W. Principles of mathematical analysis (1976), McGraw-Hill, Singapore