Evaluating Volterra Integro-Differential Equations in terms of Global, Polynomial and Numerical Equations in Boundary Conditions
The integro-differential equations are originated from different mathematical models for many scientific phenomena. Nonlinear integro-differential equations are also can be seen in various applications of various scientific fields that are modeled by nonlinear phenomena.
The solutions using in integro-differential equations have an important role in lots of engineering fields, also in financial problems, physics theories. The major area of integro-differential –equations are especially mechanical engineering, electric-electronic engineering, economics. Boundary conditions are very important for Volterra equations in order to make them more visual. Furthermore the benefit working on boundary conditions is to see excellent satability properties and high accuracy for Volterra equations. In addition, while evaluating integro differential equations, we should consider the situations about nonlinear integro-differential equations. Nonlinear integro differential equations are essential also in several fields. For instance, fluid dynamics, polymer science, population dynamics, thermoelasticity, chemical engineering can be researching area.
Because to solve a problem analytically can be very hard and spend a lot of time, global, polynomial and numerical methods can be very useful. However, in last decades, numerical methods have been used by many scientists. These numerical methods can be listed like The Taylor-series expansion method, the hybrid function method, Adomian decomposition method, The Legendre wavelets method, The Tau method, The finite difference method, The Haar function method, The...
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...initial value problems. To acquire global solution for differential equations in general, the concept of fuzzy linear differential equation is utilized. 
To conclude, with the increasing development which is used in the engineering, mechanics, physics, chemistry and astronomy, integro-differential equations are an indispensable major of mathematics. One of the most important equations, Volterra integro differential equations have various solutions by global, polynomial and numerical. These solutions have different various advantages and disadvantages for using different scientific fields. While one type of a solution is useful engineering, another solution is better for astronomy. Because of these reasons, to know every detail about methods for Volterra integro equations, to comprehend the principles of equations for being a good scientist is very essential.