Solutions of Volterra Integral Equations of Second Kind Using Various Method

Integral equations are powerful mathematical tools used to model and solve a vast array of ‎real-world problems. Their ability to transform and simplify complex systems makes them ‎essential in theoretical and applied sciences. Volterra integral equations are essential for ‎modeling time-dependent, causal, and memory-influenced systems. They are mathematically ‎tractable and appear in a wide variety of scientific and engineering contexts. 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 thermodynamics, biology, chemistry, medical sciences, physics, heat flow, neutron diffusion ‎problem, electric circuit problem, transform problem mechanics, engineering can represent ‎mathematically in terms of volterra integral equation of first kind and second kind. We used ‎Successive approximation method; Variational iterative method and Laplace transform Method ‎for solving volterra integral equations of second kind‎.