Editorial: Analytical and Numerical Methods for Differential Equations and Applications

Numerical methods for differential equations and applications

In the contemporary language of mathematics, a special place is occupied by Numerical Analysis, thanks to the steadily developing interest for the interplay among abstract formalism, computations and simulation of real world phenomena. This research contribution means to offer an example of such conceptual interplay. In particular, main research activity of Ivonne Sgura in 2012 deals with the d...

global results on some nonlinear partial differential equations for direct and inverse problems

در این رساله به بررسی رفتار جواب های رده ای از معادلات دیفرانسیل با مشتقات جزیی در دامنه های کراندار می پردازیم . این معادلات به فرم نیم-خطی و غیر خطی برای مسایل مستقیم و معکوس مورد مطالعه قرار می گیرند . به ویژه، تاثیر شرایط مختلف فیزیکی را در مساله، نظیر وجود موانع و منابع، پراکندگی و چسبندگی در معادلات موج و گرما بررسی می کنیم و به دنبال شرایطی می گردیم که متضمن وجود سراسری یا عدم وجود سراسر...

Comparison of acceleration techniques of analytical methods for solving differential equations of integer and fractional order

The work  addressed in this paper is a comparative study between convergence of the  acceleration techniques, diagonal pad'{e} approximants and shanks transforms, on Homotopy analysis method  and Adomian decomposition method for solving  differential equations of integer and fractional orders.

Numerical Methods for Differential Equations

Numerical Methods for Differential Equations

After revisiting some practical problems of numerical methods by playing with models introduced in Chapter 2, we will investigate the two most important properties of numerical algorithms—stability and accuracy. This is done most easily in the context of the simplest numerical method, i.e., the explicit Euler method (Section 5.2). The problem of solving stiff differential equations is addressed...