Ride the Storm: Navigating Through Unstable Periods / Katerina Rudko (Belka G...
Integral Equations PPT Unit-III
1. UNIT-III
VOLTERRA INTEGRAL EQUATIONS
Types of Voltera equations. Resolvent kernel of Voltera
equations, Convolution type kernels. Some miscellaneous types
of Voltera equations. Non-linear Voltera equations. Fourier
integral equations. Laplace integral equations.
6. Type 1. Determination of resolvent kernel or reciprocal kernel
for Volterra integral equation
7.
8.
9.
10. Type 2: Solution of Volterra Integral Equation of the Second
Kind with the help of Resolvent Kernel
• Consider the following Volterra integral equation
86. Nonlinear Volterra Integral Equations
• The nonlinear Volterra equations are characterized by at least one variable
limit of integration. In the nonlinear Volterra integral equations of the second
kind, the unknown function u(x) appears inside and outside the integral sign.
• The nonlinear Volterra integral equation of the second kind is represented by
the form
However, the nonlinear Volterra integral equations of the first kind contains
the nonlinear function F(u(x)) inside the integral sign. The nonlinear Volterra
integral equation of the first kind is expressed in the form