Integro-Differential Equations

Integro-Differential Equations

 

equations containing both integrals and derivatives of an unknown function. An example is the equation obtained by the Italian mathematician V. Volterra in the problem of torsional oscillations:

Sometimes integro-differential equations can be reduced to integral equations or differential equations. A solution to an integro-differential equation may be sought by the method of successive approximations.

References in periodicals archive ?
Work is was performed as part of the scientific program for basic research RK Ministry of Education "Solution new mathematical methods of nonlinear differential and integro-differential equations of fundamental and applied problems of mechanics of solid and deformable solids" (Contractfor research No.
Kanagarajan, Existence of solutions of fuzzy delay integro-differential equations with nonlocal condition, Journal of the Korea Society for Industrial and Applied Mathematics, 9 (2005) 65-74.
Beginning with a section on basic definitions, the work covers elementary methods for solving singular integral equations, Riemann-Hilbert problems, hypersingular integral equations, singular integro-differential equations, the Galerkin method and several numerical methods.
Muresan, Application of a trapezoid inequality to neutral Fredholm Integro-differential equations in Banach spaces, J.
It is known that integro-differential equations arise from many fields of science, for example in applied areas which include engineering, mechanics, financial mathematics, etc.
He covers Volterra integral equations, Fredholm integral equations, nonlinear integral equations, the singular integral equation, integro-differential equations, symmetric kernals and orthogonal systems of functions, and a range of applications.
The Abel equation is discussed in [18], the Hammerstein equation in [21,22], integro-differential equations are considered in [23].
Wavelet-Galerkin method for integro-differential equations.
By employing vector Liapunov-like functions, a generalised variation of constant formula is developed to study the perturbed linear integro-differential equations.
Covered in the 2004 edition are the calculation of linear least squares, the numerical analysis of functional integral and integro-differential equations of Volterra type, sparse grids, complete search in continuous global optimization and constraint satisfaction, and multiscale computational modeling of the heart.
Keywords and Phrases: Integro-differential equations, A priori bound on solutions, Essential maps, Topological transversality theorem.
Theory of functionals and of integral and integro-differential equations.