Refine your search
Collections
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z All
Ezzati, R.
- Application of Chebyshev Polynomials for Solving Nonlinear Volterra-fredholm Integral Equations System and Convergence Analysis
Abstract Views :587 |
PDF Views:108
Authors
Affiliations
1 Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, IR
1 Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, IR
Source
Indian Journal of Science and Technology, Vol 5, No 2 (2012), Pagination: 2060-2064Abstract
In this paper, we solve the nonlinear Volterra-Fredholm integral equations system by using the Chebyshev polynomials. First we introduce the Chebyshev polynomials and approximate functions via their application. Then, we use Chebyshev polynomials as a collocation basis to change the nonlinear Volterra-Fredholm integral equations system to a system of nonlinear algebraic equations. Finally, the convergence analysis is considered, and numerical examples given to illustrate the efficiency of this method.Keywords
Volterra-fredholm, System of Integral Equations, Chebyshev Polynomials, Operational MatrixFull Text
References
- Brunner H (1990) On the numerical solution of nonlinear Volterra-Fredholm integral equations by collocation methods. SIAM J. Num. Anal. Vol.27 N0.4 987-1000.
- Cerdik-Yaslan H and Akyuz-Dascioglu A (2006) Chebyshev polynomial solution of nonlinear Fredholm-Volterra integro-differential equations. J. Arts. Sci. 5, 89-101.
- Chihara TS (1978) An Introduction to Orthogonal Polynomials, Gordon and Breach Sci. Publ. Inc., NY.
- Chuong NM and Tuan NV (1996) Spline collocation methods for a system of nonlinear Fredholm-Volterra integral equations. Acta. Math. Viet. 21, 155-169.
- Delves LM and Mohamed JL (1985) Computional methods for Integral equations. Cambridge Univ. Press, Cambridge.
- Ezzati R and Najafalizadeh S (2011) Numerical solution of nonlinear Volterra-Fredholm integral equation by using Chebyshev polynomials. Math. Sci. Quartery J. 5, 1-12.
- Jumarhan B and Mckee S (1996) Product integration methods for solving a system of nonlinear Volterra integral equatin J. Comput. Math. 69, 285-301.
- Maleknejad K and Fadaei Yami MR (2006) A computational method for system of Volterra-Fredholm integral equations. Appl. Math. Comput. 188, 589-595.
- Maleknejad K and Mahmodi Y (2003) Taylor polynomial solution of high-order nonlinear Volterra-Fredholm integrodifferential equations. Appl. Math. Comput. 145, 641-653.
- Maleknejad K, Sohrabi S and Rostami Y (2007) Numerical solution of nonlinear Volterra integral equation of the second kind by using Chebyshev polynomials. Appl. Math. Comput. 188 ,123-128.
- Rabbani M, Maleknejad K and N Aghazadeh (2007) Numerical computational solution of the Volterra integral equations system of the second kind by using an expansion method.Appl. Math. Comput. 187, 1143-1146.
- Rao GP (1983) Control and Information sciences. Springer-Verlag., Berlin. 49, 96-110.
- Yalsinbas S (2002) Taylor polynomial solution of nonlinear Volterra-Fredholm integral equations. Appl. Math. Comput. 127, 195-206.
- Approximate Symmetric Solution of Dual Fuzzy Systems Regarding Two Different Fuzzy Multiplications
Abstract Views :428 |
PDF Views:121
Authors
Affiliations
1 Department of Mathematics, Roudehen Branch, Islamic Azad University, Roudehen, IR
2 Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, IR
3 Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj
1 Department of Mathematics, Roudehen Branch, Islamic Azad University, Roudehen, IR
2 Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, IR
3 Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj
Source
Indian Journal of Science and Technology, Vol 5, No 2 (2012), Pagination: 2100-2112Abstract
We consider two types of dual fuzzy systems with respect to two different fuzzy multiplications and propose an approach for computing an approximate nonnegative symmetric solution of some dual fuzzy linear system of equations. We convert the m × n dual fuzzy linear system to two m × n real linear systems by considering equality of the median intervals of the left and right sides of the dual fuzzy system. Then, the real systems are solved, when the solutions does not satisfy nonnegative fuzziness conditions, an appropriate constrained least squares problem is solved. We finally present some computational algorithms and illustrate their effectiveness by solving some randomly generated consistent as well as inconsistent systems.Keywords
LR Fuzzy Numbers, Triangular Fuzzy Numbers, Dual Fuzzy Systems, Median Interval DefuzzificationFull Text
References
- Abbasbandy S, Asady B and Alavi M (2005) Fuzzy general linear systems. Appli. Math. Comput. 169, 34- 40.
- Abbasbandy S, Ezzati R and Jafarian A (2006) LU decomposition method for solving fuzzy system of linear equations. Appl. Math. Comput. 172, 633-643.
- Allahviranloo T (2008) Revised solution of an overdetermined fuzzy linear system of equations.Intl. J. Comput. Cognition. 6(3), 66-70.
- Allahviranloo T, Ahmady E, Ahmady N and Shams Alketaby Kh (2006) Block Jacobi two-stage method with Gauss-Sidel inner iterations for fuzzy system oflinear equations. Appl. Math. Comput. 175, 1217- 1228.
- Bodjanova S (2005) Median value and median interval of a fuzzy number. Inf. Sci. 172, 73-89.
- Buckley JJ and Qu Y (1991) Solving system of linear fuzzy equations. Fuzzy Set. Syst. 43, 33-43.
- Chang SL and Zadeh LA (1972) On fuzzy mapping and control. IEEE Trans. Syst. Man. Cyb. 2, 30-34.
- Dehghan M and Hashemi B (2007) Iterative the solution of fuzzy linear systems. Chaos Soliton Fract.34, 316-336.
- Dehghan M and Hashemi B (2006a) Solution of the fully fuzzy linear systems using the decomposition procedure. Appl. Math. Comput. 182, 1568-1580.
- Dehghan M, Hashemi B and Ghatee M (2006b) Computational methods for solving fully fuzzy linear systems. Appl. Math. Comput. 179, 328-343.
- Dehghan M, Hashemi B and Ghatee M (2006c) Solution of the fully fuzzy linear systems using iterative techniques. Appl. Math. Comput. 175, 645-674.
- Dubois D and Prade H (1980) Fuzzy Sets and Systems. Theory & Appli. Acad. Press, NY.
- Ezzati R (2008) , A method for solving dual fuzzy general linear systems. Appl. Comput. Math. (7) 2,235-241.
- Ezzati RandAbbasbandy S (2007) Newton's method for solving a system of dual fuzzy nonlinear equations. Math. Sci. Quart. J. 1, 71-82.
- Ezzati R, Khezerloo S, Mahdavi-Amiri N and Valizadeh Z (2012) New models and algorithms for approximate solutions of single-signed fully fuzzy LR linear systems. Iran. J. Fuzzy Syst. (in press).
- Friedman M, Ming M and Kandel A (1998) Fuzzy linear systems. Fuzzy Set. Syst. 96, 201-209.
- Ghanbari R, Mahdavi-Amiri N and Yousefpour R (2010) Exact and approximate solutions of fuzzy LR linear systems: New algorithms using a least squares model and ABS approach. Iran. J. Fuzzy Syst. 7(2), 1- 18.
- Kauffman A and Gupta MM (1991) Introduction to fuzzy arithmetic: Theory and application. Van Nostrand Reinhold, NY.
- Ming M, Friedman M and Kandel A (2000) Duality in fuzzy linear systems. Fuzzy Set Syst. 109(1), 55-58.
- Muzzioli S and Reynaerts H (2006) Fuzzy linear systems of the form 1 1 2 2 A x b = A x b . Fuzzy Set. Syst. 157 (7), 939-951.
- Zadeh LA (1972) A fuzzy-set-theoretic interpretation of linguistic hedges. J. Cybernetics. 2, 4-34.
- Zadeh LA (1975) The concept of the linqustic variable and its application to approximate reasoning. Inf. Sci. 8, 199-249.
- Zimmermann HJ (1991) Fuzzy set theory and its applications. Kluwer Acad.Press, Dordrecht .
- A New Approach to the Numerical Solution of Fredholm-Volterra Integral Equations by Using Multiquadric Quasi-interpolation
Abstract Views :499 |
PDF Views:97
Authors
R. Ezzati
1,
K. Shakibi
1
Affiliations
1 Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, IR
1 Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, IR
Source
Indian Journal of Science and Technology, Vol 5, No 5 (2012), Pagination: 2733-2737Abstract
In this paper, we introduce an approach for solving Fredholm-Volterra integral equations(FVIE) of the second kind by using Multiquadric quasi-interpolation (MQ). Approximation of unknown function is done by using expansion method based on MQ. This method obtains acceptable approximate solution using simple computations. Also we prove a theorem for convergence analysis. We test the proposed method in some examples and compare the numerical and exact results.Keywords
Radial Basis Function, Quasi-interpolation, Fredholm-volterra Integral Equations, Numerical MethodFull Text
References
- Beatson RK and Powell MJD (1992) Univariate MQ approximation quasi-interpolation to scattered data. Constr. 8 275-288.
- Chen R, XHan Z and Wu (2009) A multiquadric quasi-interpolation with linear reproducing and preserving monotonicity. J. Computational & Appl. Math. 231,517-525.
- Hardy RL (1971) Multiquadric equation of topography and other irregular surfaces. Geophys.Res. 76,1905- 1915.
- Hardy RL 1990 Theory and application of the multiquadric-biharmonic method, 20 years of discovery 1968-1988. Math. Appl. 19,163-208.
- Kansa EJ (1990) Multiquadrics-a scattered data approximation scheme with applications to computational fluid dynamics 1. Math. Appl. 19,127- 145.
- Maleknejad K, Hashemizadeh E and Ezzati R (2011) A new approach to numerical solution of Valterra integral equations by using Bernstien's approximation. Commun. Nounlinear Sci. Numer.Simulate. 16,647-655.
- Wu ZM and Schaback R (1994) Shape preserving properties and convergence of univariate multiquadric quasi-interpolation. Acta Math. Appl.Sin. 10,441-446.
- Numerical Solution of Backward Stochastic Differential Equations Driven by Brownian Motion through Block Pulse Functions
Abstract Views :295 |
PDF Views:0
Authors
Affiliations
1 Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, IR
1 Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, IR
Source
Indian Journal of Science and Technology, Vol 7, No 3 (2014), Pagination: 271–275Abstract
In this paper, a computational technique is presented for solving a Backward Stochastic Differential Equations (BSDEs) driven by a standard Brownian motion. The proposed method is stated via a stochastic operational matrix based on the Block Pulse Functions (BPFs) in combination with the collocation method. With using this approach, the BSDEs are reduced to a stochastic nonlinear system of 2m equations and 2m unknowns. Then, the error analysis is proved by using some definitions, theorems and assumptions on the BSDEs. Efficiency of this method and good reasonable degree of accuracy is confirmed by some numerical examples.Keywords
Backward Stochastic Differential Equations, Block Pulse Function, Brownian Motion, Stochastic Operational MatrixFull Text