Recent Progress in Differential and Difference Equations

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 ...

Recent Progress in Allergen Immunotherapy

The efficacy of allergen immunotherapy for the treatment of allergic rhinoconjunctivitis with or without seasonal bronchial asthma and anaphylaxis caused by the sting of the hymenoptera class of insects has been clearly demonstrated in numerous well-designed, placebo-controlled trials. Immunotherapy whether by subcutaneous injection of allergen extract or by oral/sublingual routes modifies peri...

Linear difference and differential equations

Finite difference method for solving partial integro-differential equations

In this paper, we have introduced a new method for solving a class of the partial integro-differential equation with the singular kernel by using the finite difference method. First, we employing an algorithm for solving the problem based on the Crank-Nicholson scheme with given conditions. Furthermore, we discrete the singular integral for solving of the problem. Also, the numerical results ob...

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...