Volterra Integral Equations on Unbounded Time Scales
نویسندگان
چکیده
منابع مشابه
Volterra integral equations on time scales: Basic qualitative and quantitative results with applications to initial value problems on unbounded domains
Abstract This article introduces the basic qualitative and basic quantitative theory of Volterra integral equations on time scales and thus may be considered as a foundation for future advanced studies in the field. New sufficient conditions are introduced that guarantee: existence; uniqueness; approximation; boundedness and certain growth rates of solutions to both linear and nonlinear problem...
متن کاملVolterra Integral Equations Governed by Highly Oscillatory Functions on Time Scales
It is well known that there are many analogies between the theories of difference equations and differential equations. The concept of time scales unifies these two situations but gives also solutions for problems on discrete sets with non-uniform step size or combinations of real and discrete intervals and many others. On the other hand, as it was seen in literature (beginning with [2]), the s...
متن کاملNumerical solution of Fredholm integral-differential equations on unbounded domain
In this study, a new and efficient approach is presented for numerical solution of Fredholm integro-differential equations (FIDEs) of the second kind on unbounded domain with degenerate kernel based on operational matrices with respect to generalized Laguerre polynomials(GLPs). Properties of these polynomials and operational matrices of integration, differentiation are introduced and are ultili...
متن کاملDiscretization of Volterra Integral Equations
We show that various (discrete) methods for the approximate solution of Volterra (and Abel) integral equations of the first kind correspond to some discrete version of the method of (recursive) collocation in the space of (continuous) piecewise polynomials. In a collocation method no distinction has to be made between equations with regular or weakly singular kernels; the regularity or nonregul...
متن کاملTime-stepping methods for Volterra-Fredholm integral equations
The semidiscretization in space of Volterra-Fredholm integral equations (arising, for example, as mathematical models of the spreading of epidemics) leads to large systems of Volterra integral equations. Here, we study inexpensive timestepping methods using certain DQ (= direct quadrature) methods which are employed in a way that exploits the local superconvergence properties of spatial colloca...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: International Journal of Difference Equations
سال: 2019
ISSN: 0974-1828,0973-6069
DOI: 10.37622/ijde/14.2.2019.169-177