A class of bases in L2 for the sparse representations of integral operators
SIAM Journal on Mathematical Analysis
An integro-differential equation arising from an electrochemistry model
Quarterly of Applied Mathematics
Adomian decomposition method for solving BVPs for fourth-order integro-differential equations
Journal of Computational and Applied Mathematics
Periodic boundary value problems for second-order impulsive integro-differential equations
Journal of Computational and Applied Mathematics
Fourth order integro-differential equations using variational iteration method
Computers & Mathematics with Applications
Computers & Mathematics with Applications
Numerical solution of nonlinear Fredholm integral equations of the second kind using Haar wavelets
Journal of Computational and Applied Mathematics
New algorithm for second-order boundary value problems of integro-differential equation
Journal of Computational and Applied Mathematics
Computers & Mathematics with Applications
Applied Numerical Mathematics
A meshless based method for solution of integral equations
Applied Numerical Mathematics
Journal of Computational and Applied Mathematics
Computers & Mathematics with Applications
The numerical solution of the non-linear integro-differential equations based on the meshless method
Journal of Computational and Applied Mathematics
A sequential approach for solving the Fredholm integro-differential equation
Applied Numerical Mathematics
Block boundary value methods for solving Volterra integral and integro-differential equations
Journal of Computational and Applied Mathematics
Mathematical and Computer Modelling: An International Journal
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
A new approach for numerical solution of integro-differential equations via Haar wavelets
International Journal of Computer Mathematics
Hi-index | 7.29 |
In this paper, a novel technique is being formulated for the numerical solution of integral equations (IEs) as well as integro-differential equations (IDEs) of first and higher orders. The present approach is an improved form of the Haar wavelet methods (Aziz and Siraj-ul-Islam, 2013, Siraj-ul-Islam et al., 2013). The proposed modifications resulted in computational efficiency and simple applicability of the earlier methods (Aziz and Siraj-ul-Islam, 2013, Siraj-ul-Islam et al., 2013). In addition to this, the new approach is being extended from IDEs of first order to IDEs of higher orders with initial- and boundary-conditions. Unlike the methods (Aziz and Siraj-ul-Islam, 2013, Siraj-ul-Islam et al., 2013) (where the kernel function is being approximated by two-dimensional Haar wavelet), the kernel function in the present case is being approximated by one-dimensional Haar wavelet. The modified approach is easily extendable to higher order IDEs. Numerical examples are being included to show the accuracy and efficiency of the new method.