Smooth formulation for isothermal compositional simulation with improved nonlinear convergence

a sequential formulation for compositional reservoirs simulation using peng robinson equation of state

OPTIMIZATION FORMULATION FOR NONLINEAR STRUCTURAL ANALYSIS

In this paper, the effect of angle between predictor and corrector surfaces on the structural analysis is investigated. Two objective functions are formulated based on this angle and also the load factor. Optimizing these functions, and using the structural equilibrium path’s geometry, lead to two new constraints for the nonlinear solver. Besides, one more formula is achieved, which was p...

Convergence of projected iterative regularization methods for nonlinear problems with smooth solutions

This paper is concerned with two aspects in the convergence analysis of regularization methods for nonlinear problems. Firstly, if a solution of the inverse problem (or its difference to an inital guess) is sufficiently smooth, the conditions on the nonlinearity of the forward operator become rather weak. Here we prove a convergence result for general regularized Newton methods that – among oth...

New iterative methods with seventh-order convergence for solving nonlinear equations

In this paper, seventh-order iterative methods for the solution ofnonlinear equations are presented. The new iterative methods are developed byusing weight function method and using an approximation for the last derivative,which reduces the required number of functional evaluations per step. Severalexamples are given to illustrate the eciency and the performance of the newiterative methods.

AN ITERATIVE METHOD WITH SIX-ORDER CONVERGENCE FOR SOLVING NONLINEAR EQUATIONS

Modification of Newtons method with higher-order convergence is presented. The modification of Newtons method is based on Frontinis three-order method. The new method requires two-step per iteration. Analysis of convergence demonstrates that the order of convergence is 6. Some numerical examples illustrate that the algorithm is more efficient and performs better than classical Newtons method and ...