Journal of Advanced Research in Applied Mathematics and Statistics

Laplace Transform for Convolution Type Linear Volterra Integral Equation of Second Kind

Raman Chauhan — 2019-11-24

Volterra integral equations appear when we convert initial value problem to an integral equation. The solution of Volterra integral equation is much easier than the original initial value problem. Many problems of science and engineering like neutron diffusion problem, heat transfer problem, radiation transfer problem, electric circuit problem etc can be represent mathematically in terms of Volterra integral equation. In the present paper, authors discussed Laplace transform for convolution type linear Volterra integral equation of second kind. In application section, some applications are given to explain the usefulness of Laplace transform for finding the solution of convolution type linear Volterra integral equation of second kind.

How to cite this article:
Chauhan R, Aggarwal S. Laplace Transform
for Convolution Type Linear Volterra Integral
Equation of Second Kind. J Adv Res Appl Math
Stat 2019; 4(3&4): 1-7.

Laplace Transform for the Solution of Abel’s Integral Equation

Dr. Nidhi Sharma — 2019-11-25

Abel’s Integral Equation is an important singular Integral Equation and generally appears in many branches of sciences such as atomic scattering, mechanics, radio astronomy, physics, electron emission, X-ray radiography and seismology. In this paper, authors discussed the Laplace transform for the solution of Abel’s Integral Equation and some numerical applications in application section are given to demonstrate the effectiveness of Laplace transform for the solution of Abel’s Integral Equation.

How to cite this article:
Sharma N, Aggarwal S. Laplace Transform for the Solution of Abel’s Integral Equation. J Adv Res Appl Math Stat 2019; 4(3&4): 8-15.

Laplace Transform for the Solution of First Kind Linear Volterra Integral Equation

Sudhanshu Aggarwal — 2019-11-25

In recent years, integral transforms have become an essential working tool of every applied scientist and engineers. Integral transforms have been used in obtaining the solution to problems governed by ordinary and partial differential equations and special types of integral equations. The basic aim of the integral transforms is to transform a given problem into one that is easier to solve. The most common use of integral transforms is finding the solution of initial value problems. However, there are many other situations for which the integral transforms are also useful, such as in the evaluation of certain integrals and in the solution of certain differential equations, partial differential equations and integral equations. In this paper, Laplace transform for the solution of first kind linear Volterra integral equation is presented and in application section of this paper, some numerical applications are given to demonstrate the effectiveness of proposed scheme.

How to cite this article:
Aggarwal S, Sharma N. Laplace Transform for the Solution of First Kind Linear Volterra Integral Equation. J Adv Res Appl Math Stat 2019; 4(3&4): 16-23.