A survey of singularly perturbed Volterra equations
Selected papers of the second international conference on Numerical solution of Volterra and delay equations : Volterra centennial: Volterra centennial
Journal of Computational Physics
A wavelet-based method for numerical solution of nonlinear evolution equations
Proceedings of the fourth international conference on Spectral and high order methods (ICOSAHOM 1998)
Haar wavelet approach to nonlinear stiff systems
Mathematics and Computers in Simulation
Rationalized Haar functions method for solving Fredholm and Volterra integral equations
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Journal of Computational Physics
International Journal of Computer Mathematics
Toeplitz matrix method and nonlinear integral equation of Hammerstein type
Journal of Computational and Applied Mathematics
Numerical solution of nonlinear Fredholm integral equations of the second kind using Haar wavelets
Journal of Computational and Applied Mathematics
Daubechies wavelet beam and plate finite elements
Finite Elements in Analysis and Design
Legendre wavelets method for the nonlinear Volterra-Fredholm integral equations
Mathematics and Computers in Simulation
A comparative study of numerical integration based on Haar wavelets and hybrid functions
Computers & Mathematics with Applications
Quadrature rules for numerical integration based on Haar wavelets and hybrid functions
Computers & Mathematics with Applications
Journal of Computational and Applied Mathematics
Application of Legendre wavelets for solving fractional differential equations
Computers & Mathematics with Applications
Chebyshev wavelets approach for nonlinear systems of Volterra integral equations
Computers & Mathematics with Applications
Application of the Chebyshev polynomial in solving Fredholm integral equations
Mathematical and Computer Modelling: An International Journal
Mathematical and Computer Modelling: An International Journal
Journal of Computational and Applied Mathematics
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Two new algorithms based on Haar wavelets are proposed. The first algorithm is proposed for the numerical solution of nonlinear Fredholm integral equations of the second kind, and the second for the numerical solution of nonlinear Volterra integral equations of the second kind. These methods are designed to exploit the special characteristics of Haar wavelets in both one and two dimensions. Formulae for calculating Haar coefficients without solving the system of equations have been derived. These formulae are then used in the proposed numerical methods. In contrast to other numerical methods, the advantage of our method is that it does not involve any intermediate numerical technique for evaluation of the integral present in integral equations. The methods are validated on test problems, and numerical results are compared with those from existing methods in the literature.