New Spectral Second Kind Chebyshev Wavelets Algorithm for Solving Linear and Nonlinear Second-Order Differential Equations Involving Singular and Bratu Type Equations

A NEW MODIFIED HOMOTOPY PERTURBATION METHOD FOR SOLVING LINEAR SECOND-ORDER FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS

In this paper, we tried to accelerate the rate of convergence in solving second-order Fredholm type Integro-differential equations using a new method which is based on Improved homotopy perturbation method (IHPM) and applying accelerating parameters. This method is very simple and the result is obtained very fast.  

Second Order Linear and Nonlinear Differential Equations'

An Algorithm for Solving Second Order Linear Homogeneous Differential Equations

In th is paper we present an algor i thm for f inding a "c losed-form" solut ion of the dil l-erential equatiofl -1"'+ ql +by, where a and b are rational functions of a complex var iable .x. provided a "c losed-form" solut ion exists. The algor i thm is so arranged that i f no solut icrn is found. then no solut ion can exist . The frrst sect ion makes precise what is meant by "c losed-form" and...

Chebyshev polynomials for solving two dimensional linear and nonlinear integral equations of the second kind

In this paper, an efficient method is presented for solving two dimensional Fredholm and Volterra integral equations of the second kind. Chebyshev polynomials are applied to approximate a solution for these integral equations. This method transforms the integral equation to algebraic equations with unknown Chebyshev coefficients. The high accuracy of this method is verified through some numeric...

Application of Chebyshev Polynomials for Solving Abel's Integral Equations of the First and Second Kind

In this paper, a numerical implementation of an expansion method is developed for solving Abel's integral equations of the first and second kind. The solution of such equations may demonstrate a singular behaviour in the neighbourhood of the initial point of the interval ofintegration. The suggested method is based on the use of Taylor series expansion to overcome the singularity which le...