فهرست مقالات Operational matrices

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  1 - A solution for Volterra Integral Equations of the First Kind Based on Bernstein Polynomials
  M. Mohamadi E. Babolian S. Yousefi
  In this paper, we present a new computational method to solve Volterra integral equations of the first kind based on Bernstein polynomials. In this method, using operational matrices turn the integral equation into a system of equations. The computed operational matrice چکیده کامل

  In this paper, we present a new computational method to solve Volterra integral equations of the first kind based on Bernstein polynomials. In this method, using operational matrices turn the integral equation into a system of equations. The computed operational matrices are exact and new. The comparisons show this method is acceptable. Moreover, the stability of the proposed method is studied. پرونده مقاله
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  2 - Solution of Nonlinear Fredholm-Volterra Integral Equations via Block-Pulse ‎Functions
  F. Abbasi M. Mohamadi
  In this paper, a new simple direct method to solve nonlinear Fredholm-Volterra integral equations is presented. By using Block-pulse (BP) functions, their operational matrices and Taylor expansion a nonlinear Fredholm-Volterra integral equation converts to a nonlinear s چکیده کامل

  In this paper, a new simple direct method to solve nonlinear Fredholm-Volterra integral equations is presented. By using Block-pulse (BP) functions, their operational matrices and Taylor expansion a nonlinear Fredholm-Volterra integral equation converts to a nonlinear system. Some numerical examples illustrate accuracy and reliability of our solutions. Also, effect of noise shows our solutions are stable. پرونده مقاله
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  3 - A Hybrid Approach for Systems of Integral ‎Equations‎
  J. Biazar Y. Parvari Moghaddam kh. Sadri
  10.30495/ijim.2023.21178
  ‎In this paper‎, ‎we present a computational method for solving systems of Volterra and Fredholm integral equations which is a hybrid approach‎, ‎based on the third-order Chebyshev polynomials and block-pulse functions which we will refer to as (HBV) چکیده کامل

  ‎In this paper‎, ‎we present a computational method for solving systems of Volterra and Fredholm integral equations which is a hybrid approach‎, ‎based on the third-order Chebyshev polynomials and block-pulse functions which we will refer to as (HBV)‎, ‎for short‎. ‎The existence and uniqueness of the solutions are addressed‎. ‎Some examples are provided to clarify the efficiency and accuracy of the method‎. پرونده مقاله
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  4 - Application of the exact operational matrices for solving the Emden-Fowler equations, arising in ‎Astrophysics‎
  S. A. Hossayni‎ J. A. Rad K. Parand S. Abbasbandy
  The objective of this paper is applying the well-known exact operational matrices (EOMs) idea for solving the Emden-Fowler equations, illustrating the superiority of EOMs over ordinary operational matrices (OOMs). Up to now, a few studies have been conducted on EOMs ; b چکیده کامل

  The objective of this paper is applying the well-known exact operational matrices (EOMs) idea for solving the Emden-Fowler equations, illustrating the superiority of EOMs over ordinary operational matrices (OOMs). Up to now, a few studies have been conducted on EOMs ; but the solved differential equations did not have high-degree nonlinearity and the reported results could not strongly show the excellence of this new method. So, we chose Emden-Fowler type differential equations and solved them utilizing this method. To confirm the accuracy of the new method and to show the preeminence of EOMs over OOMs, the norm 1 of the residual and error function for both methods are evaluated for multiple $m$ values, where $m$ is the degree of the Bernstein polynomials. We report the results by some plots to illustrate the error convergence of both methods to zero and also to show the primacy of the new method versus OOMs. The obtained results demonstrate the increased accuracy of the new ‎method.‎ پرونده مقاله
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  5 - The Operational matrices with respect to generalized Laguerre polynomials and their applications in solving linear differential equations with variable coefficients
  Z Kalateh Bojdi S Ahmadi-Asl A Aminataei
  In this paper, a new and ecient approach based on operational matrices with respect to the gener-alized Laguerre polynomials for numerical approximation of the linear ordinary dierential equations(ODEs) with variable coecients is introduced. Explicit formulae which e چکیده کامل

  In this paper, a new and ecient approach based on operational matrices with respect to the gener-alized Laguerre polynomials for numerical approximation of the linear ordinary dierential equations(ODEs) with variable coecients is introduced. Explicit formulae which express the generalized La-guerre expansion coecients for the moments of the derivatives of any dierentiable function in termsof the original expansion coecients of the function itself are given in the matrix form. The mainimportance of this scheme is that using this approach reduces solving the linear dierential equationsto solve a system of linear algebraic equations, thus greatly simplify the problem. In addition, severalnumerical experiments are given to demonstrate the validity and applicability of the method. پرونده مقاله
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  6 - Numerical solution of Fredholm integral-differential equations on unbounded domain
  M. Matinfar A. Riahifar
  In this study, a new and efficient approach is presented for numerical solution ofFredholm integro-differential equations (FIDEs) of the second kind on unbounded domainwith degenerate kernel based on operational matrices with respect to generalized Laguerrepolynomials(G چکیده کامل

  In this study, a new and efficient approach is presented for numerical solution ofFredholm integro-differential equations (FIDEs) of the second kind on unbounded domainwith degenerate kernel based on operational matrices with respect to generalized Laguerrepolynomials(GLPs). Properties of these polynomials and operational matrices of integration, differentiation are introduced and are ultilized to reduce the (FIDEs) to the solution ofa system of linear algebraic equations with unknown generalized Laguerre coefficients. Inaddition, two examples are given to demonstrate the validity, efficiency and applicability ofthe technique. پرونده مقاله
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  7 - Operational matrices with respect to Hermite polynomials and their applications in solving linear differential equations with variable coefficients
  Z. Kalateh Bojdi S. Ahmadi-Asl A. Aminataei
  In this paper, a new and efficient approach is applied for numerical approximationof the linear differential equations with variable coeffcients based on operational matriceswith respect to Hermite polynomials. Explicit formulae which express the Hermite expansioncoeffc چکیده کامل

  In this paper, a new and efficient approach is applied for numerical approximationof the linear differential equations with variable coeffcients based on operational matriceswith respect to Hermite polynomials. Explicit formulae which express the Hermite expansioncoeffcients for the moments of derivatives of any differentiable function in terms of theoriginal expansion coefficients of the function itself are given in the matrix form. The mainimportance of this scheme is that using this approach reduces solving the linear differentialequations to solve a system of linear algebraic equations, thus greatly simplifying the problem.In addition, two experiments are given to demonstrate the validity and applicability of the method. پرونده مقاله
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  8 - Jacobi Operational Matrix Approach for Solving Systems of Linear and Nonlinear Integro-Differential Equations
  Khadijeh Sadri Zainab Ayati
  ‎‎‎‎‎‎‎‎‎‎‎‎‎This paper aims to construct a general formulation for the shifted Jacobi operational matrices of integration and product‎. ‎The main aim is to generalize the Jacobi integral and product operationa چکیده کامل

  ‎‎‎‎‎‎‎‎‎‎‎‎‎This paper aims to construct a general formulation for the shifted Jacobi operational matrices of integration and product‎. ‎The main aim is to generalize the Jacobi integral and product operational matrices to the solving system of Fredholm and Volterra integro--differential equations‎ which appear in various fields of science such as physics and engineering. ‎The Operational matrices together with the collocation method are applied to reduce the solution of these problems to the solution of a system of algebraic equations‎. ‎ Indeed, to solve the system of integro-differential equations, a fast algorithm is used for simplifying the problem under study. ‎The method is applied to solve system of linear and nonlinear Fredholm and Volterra integro-differential equations‎. ‎Illustrative examples are included to demonstrate the validity and efficiency of the presented method‎. It is further found that the absolute errors are almost constant in the studied interval. ‎Also‎, ‎several theorems related to the convergence of the proposed method‎, ‎will be presented‎‎.‎ پرونده مقاله
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  9 - Approximate solution of system of nonlinear Volterra integro-differential equations by using Bernstein collocation method
  Sara Davaeifar Jalil Rashidinia
  This paper presents a numerical matrix method based on Bernstein polynomials (BPs) for approximate the solution of a system of m-th order nonlinear Volterra integro-differential equations under initial conditions. The approach is based on operational matrices of BPs. Us چکیده کامل

  This paper presents a numerical matrix method based on Bernstein polynomials (BPs) for approximate the solution of a system of m-th order nonlinear Volterra integro-differential equations under initial conditions. The approach is based on operational matrices of BPs. Using the collocation points,this approach reduces the systems of Volterra integro-differential equations associated with the given conditions, to a system of nonlinear algebraic equations. By solving such arising non linear system, the Bernstein coefficients can be determined to obtain the finite Bernstein series approach. Numerical examples are tested and the resultes are incorporated to demonstrate the validity and applicability of the approach. Comparisons with a number of conventional methods are made in order to verify the nature of accuracy and the applicability of the proposed approach. Keywords: Systems of nonlinear Volterra integro-differential equations; The Bernstein polyno- mials and series; Collocation points. 2010 AMS Subject Classication: 34A12, 34A34, 45D05, 45G15, 45J05, 65R20. پرونده مقاله