TYPE 2- Volterra integral Equation with examples

the Volterra integral equations are a special type of integral equations. They are divided into two groups referred to as the first and the second kind. In operator theory, and in Fredholm theory, the corresponding operators are called Volterra operators.

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The standard form of Volterra linear integral equations, where the limits of integration
are functions of x rather than constants, are of the form as mention in video.
where the unknown function u(x) under the integral sign occurs linearly as stated before.
It is worth noting that (10) can be viewed as a special case of Fredholm integral
equation when the kernel K(x, t) vanishes for t is greater than x, x is in the range of integration [a, b].
As in Fredholm equations, Volterra integral equations fall under two kinds,
depending on the value of (x), namely
When phi(x)=0, it is of first kind
When phi(x)=1, it is of second kind

In summary, the Volterra integral equation is of the first kind if the unknown function
u(x) appears only under the integral sign. However, the Volterra integral equation is of
the second kind if the unknown function u(x) appears inside and outside the integral
sign.


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what is volterra integral equation
Volterra integral equation is of two type
Volterra integral equation first kind
Volterra integral equation of second kind
Examples of volteraa integral equation
Volterra integral equation hindi
Volterra integral equaiton urdu
Volterra integral equation is an type of integral equation
Definition of volterra integral equation