- (b) Volterra and Fredholm types of equation
If the limits of integration in an integral equation are fixed, the equation is called a Fredholm equation.
Alternatively if the variable occurs in the limits of integration, the equation is called a volterra equation. What are systems of integral equations?
A system of integral equations is a set of two or more integral equations in two or more unknown functions.
Usually, all of the equations belonging to a system are of the same type, but this need not be the case..
What are the various methods to solve integral and differential equations?
There are various techniques for solving a system of integral or integro-differential equation, e.g.
Adomian decomposition method (ADM) [1], [2], Galerkin method [3], rationalized Haar functions method [4], He's homotopy perturbation method (HPM) [5], [6] and variational iteration method (VIM) [7]..
What is the collocation method for solving integral equations?
Collocation method involves evaluating of approximate solution in a suitable set of functions called basis function or trial solution.
This method for obtaining the approximate solution to an integral equation has its origin in the 1930s when [3] consider an integral equation using the line collocation procedure..
Why do we integrate equations?
Integration is basically used to find the areas of the two-dimensional region and computing volumes of three-dimensional objects.
Therefore, finding the integral of a function with respect to x means finding the area to the X-axis from the curve..
- A specific application of Fredholm equation is the generation of photo-realistic images in computer graphics, in which the Fredholm equation is used to model light transport from the virtual light sources to the image plane.
The Fredholm equation is often called the rendering equation in this context. - A system of integral equations is a set of two or more integral equations in two or more unknown functions.
Usually, all of the equations belonging to a system are of the same type, but this need not be the case.
