# Integro-Differential Equations

The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

## 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 ?
Numerical algorithm for solving two-point, second-order periodic boundary value problems for mixed integro-differential equations. Applied Mathematics and Computation, 243:911-922, 2014.
He discusses theory on the separable approximation of multivariate functions, multi-linear algebra and nonlinear tensor approximation, super-fast computations using quantized tensor approximation, and a tensor approach to multidimensional integro-differential equations. ([umlaut] Ringgold, Inc., Portland, OR)
An improved method based on Haar wavelets for numerical solution of nonlinear integral and integro-differential equations of first and higher orders.
Gouyandeh, "Fuzzy fractional integro-differential equations under generalized Caputo differentiability," Annals of Fuzzy Mathematics and Informatics, vol.
For example, in [15], FDTM is applied for fractional differential equations and in [16] it is used for fractional integro-differential equations. This method is applied to nonlinear fractional partial differential equations in [17].
Day, "Note on the Numerical Solution of Integro-Differential Equations," The Computer Journal, vol.
Systems of integro-differential equations and their solutions play a pivotal role in the fields of science, industrial mathematics, control theory of financial mathematics, and engineering [1-3].
Many physical phenomena in different fields of sciences and engineering have been formulated using integro-differential equations. The nonlinear integro-differential equations play a crucial role to describe many process like fluid dynamics, biological models and chemical kinetics, population, potential theory, polymer theology, and drop wise condensation (see [1-4] and the references cited therein).
Peng, "Nonlinear impulsive integro-differential equations of mixed type and optimal controls," Optimization.
During the last years, many good results have been obtained on the qualitative behaviors in Volterra integro-differential equations without delay.
El-Azab, "Legendre-Galerkin method for the linear Fredholm integro-differential equations," Applied Mathematics and Computation, vol.
Grimmer, "Propagation of singularities for integro-differential equations," Journal of Differential Equations, vol.

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