Semidiscretization schemes for the autonomous differential equations with noncompact semigroups using functionalizing parameter method

Nonstandard finite difference schemes for differential equations

In this paper, the reorganization of the denominator of the discrete derivative and nonlocal approximation of nonlinear terms are used in the design of nonstandard finite difference schemes (NSFDs). Numerical examples confirming then efficiency of schemes, for some differential equations are provided. In order to illustrate the accuracy of the new NSFDs, the numerical results are compared with ...

nonstandard finite difference schemes for differential equations

in this paper, the reorganization of the denominator of the discrete derivative and nonlocal approximation of nonlinear terms are used in the design of nonstandard finite difference schemes (nsfds). numerical examples confirming then efficiency of schemes, for some differential equations are provided. in order toillustrate the accuracy of the new nsfds, the numerical results are compared with s...

Method of semidiscretization in time to nonlinear retarded differential equations with nonlocal history conditions

where 0< τ , T <∞, φ0 ∈ 0 := C([−τ,0];H), the nonlinear operator A is single valued andmaximalmonotone defined from the domainD(A)⊂H intoH, the nonlinearmap f is defined from [0,T ]×Hm+1 into H, the map h is defined from 0 into 0, and ψ[−τ,0] is the restriction of ψ ∈ T := C([−τ,T];H) on [−τ,0]. Here t := C([−τ,t];H) for t ∈ [0,T ] is the Banach space of all continuous functions from [−τ,t] int...

Parameter identification for deterministic and stochastic differential equations using the “collage method” for fixed point equations

Solutions to Nonlocal Fractional Differential Equations Using a Noncompact Semigroup

This article concerns the existence of solutions to nonlocal fractional differential equations in Banach spaces. By using a type of newly-defined measure of noncompactness, we discuss this problem in general Banach spaces without any compactness assumptions to the operator semigroup. Some existence results are obtained when the nonlocal term is compact and when is Lipschitz continuous.