This article presents a finite difference method of order two for stiff differential equation that will overcome the effects stiffness since it is A-stable. And, reflect asymptotic behavior solution problem L-stable. The classical explicit Runge–Kutta methods are not suitable problems numerical and (for example, Dahlquist problem). they both A-stable On applying Euler’s implicit method, problem...

Let L be a second order elliptic differential operator on a Riemannian manifold E with no zero order terms. We say that a function h is L-harmonic if Lh = 0. Every positive L-harmonic function has a unique representation

Propagation criterion of degree l and order k (PC(l) of order k) for Boolean functions is important for the design of block ciphers. In [1-2] Kurosawa , Stoh and Carlet give several constructions of Boolean functions satisfying PC(l) of order k from binary linear or nonlinear codes.

Robertson and Seymour proved that every graph with sufficiently large treewidth contains a large grid minor. However, the best known bound on the treewidth that forces an l × l grid minor is exponential in l. It is unknown whether polynomial treewidth suffices. We prove a result in this direction. A grid-like-minor of order l in a graph G is a set of paths in G whose intersection graph is bipar...

Variable-step (VS) second derivative $k$-step $3$-stage Hermite--Birkhoff--Obrechkoff (HBO) methods of order $p=(k+3)$, denoted by HBO$(p)$ are constructed as a combination of linear $k$-step methods of order $(p-2)$ and a second derivative two-step diagonally implicit $3$-stage Hermite--Birkhoff method of order 5 (DIHB5) for solving stiff ordinary differential equations. The main reason for co...

Robertson and Seymour proved that every graph with sufficiently large treewidth contains a large grid minor. However, the best known bound on the treewidth that forces an l × l grid minor is exponential in l. It is unknown whether polynomial treewidth suffices. We prove a result in this direction. A grid-like-minor of order l in a graph G is a set of paths in G whose intersection graph is bipar...