chatterbug219 said:Okay, understandable...but how do I start the problem? I'm still confused about how to start...
Integro-differential equations are mathematical equations that involve both derivatives and integrals. They are used to model systems in which the behavior of a variable is dependent on both its current value and its past values.
Integro-differential equations have a wide range of applications in various fields of science and engineering, such as fluid dynamics, heat transfer, quantum mechanics, and population dynamics. They are also used in the study of complex systems and in the development of mathematical models.
Integro-differential equations can be solved analytically or numerically. Analytical solutions involve finding an exact formula for the solution, while numerical solutions involve approximating the solution using numerical methods such as finite difference, finite element, or spectral methods.
Integro-differential equations can be challenging to solve due to their complex nature and the presence of both derivatives and integrals. The lack of closed-form solutions for many integro-differential equations also makes it necessary to use numerical methods, which can be computationally intensive.
Integro-differential equations are a generalization of ordinary and partial differential equations. They can be reduced to these simpler types of equations in certain cases, such as when the integral term is equal to zero. Integro-differential equations are also closely related to fractional differential equations, which involve derivatives of non-integer order.