Normalized implicit methods for the solution of non-linear elliptic boundary value problems

Parallel Solution of Elliptic Boundary Value Problems

We describe the development of some parallel iterative techniques for solving boundary value problems for elliptic partial differential equations. Using domain decomposition techniques, we modify standard sequential iterative techniques to obtain effective parallel methods. We contrast implementations on distributed-memory and shared-memory scalable parallel processors. We describe the use of t...

Quasi-linear elliptic boundary value problems

Implicit One-step L-stable Generalized Hybrid Methods for the Numerical Solution of First Order Initial Value problems

In this paper, we introduce the new class of implicit L-stable generalized hybrid methods for the numerical solution of first order initial value problems. We generalize the hybrid methods with utilize ynv directly in the right hand side of classical hybrid methods. The numerical experimentation showed that our method is considerably more efficient compared to well known methods used for the n...

Solutions for some non-linear fractional differential equations with boundary value problems

In recent years, X.J.Xu [1] has been proved some results on mixed monotone operators.  Following the paper of X.J.Xu, we study the existence and uniqueness of the positive solutions for non-linear differential equations with boundary value problems. 

SOME BOUNDARY VALUE PROBLEMS FOR A NON-LINEAR THIRD ORDER O.D.E.

Existence of periodic solutions for non-linear third order autonomous differential equation (O.D.E.) has not been investigated to as large an extent as non-linear second order. The popular Poincare-Bendixon theorem applicable to second order equation is not valid for third order equation (see [3]). This conclusion opens a way for further investigation.