Generalized Gaussian quadrature rules for systems of arbitrary functions
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Hybrid Gauss-Trapezoidal Quadrature Rules
SIAM Journal on Scientific Computing
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
Numerical solution of the controlled Duffing oscillator by hybrid functions
Applied Mathematics and Computation
Numerical solution of differential equations using Haar wavelets
Mathematics and Computers in Simulation
International Journal of Computer 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
Hybrid function method for solving Fredholm and Volterra integral equations of the second kind
Journal of Computational and Applied Mathematics
A comparative study of numerical integration based on Haar wavelets and hybrid functions
Computers & Mathematics with Applications
Mathematical and Computer Modelling: An International Journal
Journal of Computational and Applied Mathematics
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In this paper Haar wavelets and hybrid functions have been applied for numerical solution of double and triple integrals with variable limits of integration. This approach is the generalization and improvement of the methods (Siraj-ul-Islam et al. (2010) [9]) where the numerical methods are only applicable to the integrals with constant limits. Apart from generalization of the methods [9], the new approach has two major advantages over the classical methods based on quadrature rule: (i) No need of finding optimum weights as the wavelet and hybrid coefficients serve the purpose of optimal weights automatically (ii) Mesh points of the wavelets algorithm are used as nodal values instead of considering the n nodes as unknown roots of polynomial of degree n. The new methods are more efficient. The novel methods are compared with existing methods and applied to a number of benchmark problems. Accuracy of the methods are measured in terms of absolute errors.