Two-Dimensional Legendre Wavelets and their Applications to Integral Equations
نویسندگان
چکیده
منابع مشابه
SOLVING NONLINEAR TWO-DIMENSIONAL VOLTERRA INTEGRAL EQUATIONS OF THE FIRST-KIND USING BIVARIATE SHIFTED LEGENDRE FUNCTIONS
In this paper, a method for finding an approximate solution of a class of two-dimensional nonlinear Volterra integral equations of the first-kind is proposed. This problem is transformedto a nonlinear two-dimensional Volterra integral equation of the second-kind. The properties ofthe bivariate shifted Legendre functions are presented. The operational matrices of integrationtogether with the produ...
متن کاملFractional-order Legendre wavelets and their applications for solving fractional-order differential equations with initial/boundary conditions
In this manuscript a new method is introduced for solving fractional differential equations. The fractional derivative is described in the Caputo sense. The main idea is to use fractional-order Legendre wavelets and operational matrix of fractional-order integration. First the fractional-order Legendre wavelets (FLWs) are presented. Then a family of piecewise functions is proposed, based on whi...
متن کاملSolving two-dimensional fractional integro-differential equations by Legendre wavelets
In this paper, we introduce the two-dimensional Legendre wavelets (2D-LWs), and develop them for solving a class of two-dimensional integro-differential equations (2D-IDEs) of fractional order. We also investigate convergence of the method. Finally, we give some illustrative examples to demonstrate the validity and efficiency of the method.
متن کاملLegendre Wavelets for Solving Fractional Differential Equations
In this paper, we develop a framework to obtain approximate numerical solutions to ordinary differential equations (ODEs) involving fractional order derivatives using Legendre wavelets approximations. The continues Legendre wavelets constructed on [0, 1] are utilized as a basis in collocation method. Illustrative examples are included to demonstrate the validity and applicability of the techn...
متن کاملNumerical Solution of Interval Volterra-Fredholm-Hammerstein Integral Equations via Interval Legendre Wavelets Method
In this paper, interval Legendre wavelet method is investigated to approximated the solution of the interval Volterra-Fredholm-Hammerstein integral equation. The shifted interval Legendre polynomials are introduced and based on interval Legendre wavelet method is defined. The existence and uniqueness theorem for the interval Volterra-Fredholm-Hammerstein integral equations is proved. Some examp...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Indian Journal of Science and Technology
سال: 2015
ISSN: 0974-5645,0974-6846
DOI: 10.17485/ijst/2015/v8i2/58075