Alcune considerazioni relative alľequazione differenztale: $$\frac{{\partial u}}{{\partial x}} + \frac{{\partial v}}{{\partial y}} + \frac{{\partial w}}{{\partial z}} = 0$$

Rendiconti del Circolo Matematico di Palermo Series 1 -     

ALTERNATING BAND CRANK-NICOLSON METHOD FOR δu／δt=δ^2u／δx^2＋δ^2u／δy^2

the Alternating Segment Crank-Nicolson scheme for one-dimensional diffusion equation has been developed in [1],and the Alternating Block Crank-Nicolson method for two-dimensional problem in [2].The methods have the advantages of parallel computing,stability and good accuracy.In this paper for the two-dimensional diffusion equation,the net region is divided into bands,a special kind of block.This method is called the alternating Band Crank-Nicolson method.     

Über die partielle Differentialgleichung $$f(x,y)\frac{{\partial z}}{{\partial x}} + g(x,y)\frac{{\partial z}}{{\partial x}} = h (x,y).$$ II

Mathematische Zeitschrift -     

Über die Existenz von Integralen der partiellen Differentialgleichung $$f(x,y)\frac{{\partial z}}{{\partial x}} + g(x,y)\frac{{\partial z}}{{\partial x}} = 0$$ in der Umgebung eines singulären Punktes

Mathematische Zeitschrift -     

On the difference equation y_{n + 1} = \frac{{\alpha + y_n^p }} {{\beta y_{n - 1}^p }} - \frac{{\gamma + y_{n - 1}^p }} {{\beta y_n^p }}

In this paper, we investigate the global stability and the periodic nature of solutions of the difference equation $y_{n + 1} = \frac{{\alpha + y_n^p }} {{\beta y_{n - 1}^p }} - \frac{{\gamma + y_{n - 1}^p }} {{\beta y_n^p }},n = 0,1,2,... $ where α, β, γ ∈ (0,∞), α(1 ? p) ? γ > 0, 0 < p < 1, every y _n ≠ 0 for n = ?1, 0, 1, 2, … and the initial conditions y?1, y0 are arbitrary positive real numbers. We show that the equilibrium point of the difference equation is a global attractor with a basin that depends on the conditions of the coefficients.