Numerical solution of nonlinear Volterra integral equations of the second kind by using Chebyshev polynomials

A new approach to homotopy perturbation method for solving systems of Volterra integral equations of first kind

“…Exact or approximate solution of integral equations has great importance because it has wide applications in scientific research. Many researchers (Golbabai and Keramati, 2008;Eslami, 2014a;Biazar et al, 2012;Biazar and Mostafa, 2011a, b;Rabbani et al, 2007;Maleknejad et al, 2007;Tahmasbi and Fard, 2008;Odibat, 2008;Maleknejad and Najafi, 2011;Biazar and Eslami, 2011;Eslami and Mirzazadeh, 2014;Eslami, 2014b;Biazar and Eslami, 2010a, b, c;2011) have solved various types of integral equations by several methods. Biazar et al (2008) solved system of Volterra integral equations of type (1) by HPM.…”

On the numerical solution of Volterra-Fredholm integral equations with logarithmic kernel using smoothing transformation

“…The elements K(x, y) = ln |x − y| is Logarithm Kernel. For solving Volterra-Fredholm integral equations, many methods with enough accuracy and efficiency have been used before by many researches [4,5,6,7,8,9,10,11,12]. Maleknejad and Fadaei Yami [8] solved the system of Volterra-Fredholm integral equations by Adomian decomposition method.…”

Solutions of Linear and Nonlinear Volterra Integral Equations Using Hermite and Chebyshev Polynomials

“…Also Shahsavaran [5 -8] solved first and second kind linear and nonlinear Volterra integral equations by collocation method while spectral method has been used by Chen and Tang [9]. Maleknejad et al [10] used Chebyshev polynomials for numerical solution of nonlinear integral equations. On the other hand, Jafari et al [11] used Legendre wavelets for the solution of system of linear integral equations.…”

“…As a result, many numerical methods have been developed for solving differential and integral equations by many researchers using various piecewise polynomials in recent years. Bellour and Rawashdeh [3] used Taylor polynomials method to solve only first kind integral equations while a recursive scheme [4] were used by Maleknejad et al for the solutions of such type of problems. Also Shahsavaran [5 -8] solved first and second kind linear and nonlinear Volterra integral equations by collocation method while spectral method has been used by Chen and Tang [9].…”