Numerical solution of nonlinear Volterra–Fredholm–Hammerstein integral equations via collocation method based on radial basis functions

K Parand, JA Rad - Applied Mathematics and Computation, 2012‏ - Elsevier
A numerical technique based on the spectral method is presented for the solution of
nonlinear Volterra–Fredholm–Hammerstein integral equations. This method is a …

On a generalized Gaussian radial basis function: Analysis and applications

N Karimi, S Kazem, D Ahmadian, H Adibi… - … analysis with boundary …, 2020‏ - Elsevier
We introduce a new infinitely smooth generalized Gaussian radial basis function (GGRBF)
involving two shape parameters: ψ (r; ϵ; ϵ 0)= φ (r; ϵ) exp (φ (r; ϵ 0)− 1), where φ (r; ϵ) is …

[HTML][HTML] Parallel LS-SVM for the numerical simulation of fractional Volterra's population model

K Parand, AA Aghaei, M Jani, A Ghodsi - Alexandria Engineering Journal, 2021‏ - Elsevier
In this paper, we develop a least-squares support vector machine (LS-SVM) for solving a
nonlinear fractional-order Volterra's population model in a closed system. The fractional …

An RBF collocation method for solving optimal control problems

H Mirinejad, T Inanc - Robotics and Autonomous Systems, 2017‏ - Elsevier
A direct solution to optimal control problems is introduced based on interpolating global
radial basis functions (RBFs) on arbitrary collocation points. In the proposed approach …

Radial basis functions methods for solving Fokker–Planck equation

S Kazem, JA Rad, K Parand - Engineering Analysis with Boundary …, 2012‏ - Elsevier
In this paper two numerical meshless methods for solving the Fokker–Planck equation are
considered. Two methods based on radial basis functions to approximate the solution of …

[HTML][HTML] Application of Bessel functions for solving differential and integro-differential equations of the fractional order

K Parand, M Nikarya - Applied Mathematical Modelling, 2014‏ - Elsevier
In this paper, a new numerical algorithm to solve the linear and nonlinear fractional
differential equations (FDE) is introduced. Fractional calculus and fractional differential …

Solving Volterra's population growth model of arbitrary order using the generalized fractional order of the Chebyshev functions

K Parand, M Delkhosh - Ricerche di Matematica, 2016‏ - Springer
Volterra's model for population growth in a closed system includes an integral term to
indicate accumulated toxicity in addition to the usual terms of the logistic equation, that …

Numerical study of astrophysics equations by meshless collocation method based on compactly supported radial basis function

K Parand, M Hemami - International Journal of Applied and Computational …, 2017‏ - Springer
In this paper, we propose compactly supported radial basis functions for solving some well-
known classes of astrophysics problems categorized as non-linear singular initial ordinary …

[HTML][HTML] Decomposition–Linearization–Sequential Homotopy Methods for Nonlinear Differential/Integral Equations

CS Liu, CL Kuo, CW Chang - Mathematics, 2024‏ - mdpi.com
In the paper, two new analytic methods using the decomposition and linearization technique
on nonlinear differential/integral equations are developed, namely, the decomposition …

Solving integral equations by ls-svr

K Parand, AA Aghaei, M Jani, R Sahleh - Learning with fractional …, 2023‏ - Springer
The other important type of problem in science and engineering is integral equations. Thus,
develo** precise numerical algorithms for approximating the solution to these problems is …