A linear multistep method for solving first order initial value problems of ordinary differential equations is presented in this paper. The approach of collocation approximation is adopted in the derivation of the scheme and then the scheme is applied as simultaneous integrator to first order initial value problems of ordinary differential equations. This implementation strategy is more accurat...

[Received 8 May 1987 and in revised form 23 May 1988] In this paper the two-dimensional flow of fresh and salt water through a homogeneous aquifer is considered. The two fluids are assumed to be separated by a sharp interface. They differ only in their specific weight. This difference induces a flow in the aquifer which in turn causes a motion of the interface. We present a mathematical formula...

We propose primal-dual path-following Mehrotra-type predictor-corrector methods for solving convex quadratic semidefinite programming (QSDP) problems of the form: minX{2X • Q(X) + C • X : A(X) = b,X 0}, where Q is a self-adjoint positive semidefinite linear operator on Sn, b ∈ Rm, and A is a linear map from Sn to Rm. At each interior-point iteration, the search direction is computed from a dens...

We propose a family of search directions based on primal-dual entropy in the contextof interior-point methods for linear optimization. We show that by using entropy based searchdirections in the predictor step of a predictor-corrector algorithm together with a homogeneousself-dual embedding, we can achieve the current best iteration complexity bound for linear opti-mization. The...

It is still difficult for traditional methods to simulate fluid-structure interaction (FSI) problems which are increasingly used to model cardiovascular system, and human organism. This contribution develops a new numerical method to analyze FSI, based on smoothed particle hydrodynamics (SPH). The Lagrangian and meshless characteristics of SPH presents distinct features to devise the method by ...

In this work a new optimized symmetric eight-step embedded predictor-corrector method (EPCM) with minimal phase-lag and algebraic order ten is presented. The method is based on the symmetric multistep method of Quinlan-Tremaine [1], with eight steps and eighth algebraic order and is constructed to solve numerically IVPs with oscillatory solutions. We compare the new method to some recently cons...

We present a numerical approach for solving the free boundary problem for the Black-Scholes equation for pricing American style of floating strike Asian options. A fixed domain transformation of the free boundary problem into a parabolic equation defined on a fixed spatial domain is performed. As a result a nonlinear time-dependent term is involved in the resulting equation. Two new numerical a...

We present a highly robust second order accurate scheme for the Euler equations and the ideal MHD equations. The scheme is of predictor-corrector type, with a MUSCL scheme following as a special case. The crucial ingredients are an entropy stable approximate Riemann solver and a new spatial reconstruction that ensures positivity of mass density and pressure. For multidimensional MHD, a new disc...

A fourth order finite-difference scheme in a two-time level recurrence relation is proposed for the numerical solution of the generalized Burgers-Huxley equation. The resulting nonlinear system, which is analyzed for stability, is solved using an improved predictor-corrector method. The efficiency of the proposed method is tested to the kink wave using both appropriate boundary values and condi...

In this paper we propose a new class of primal-dual path-following interior point algorithms for solving monotone linear complementarity problems. At each iteration, the method would select a target on the central path with a large update from the current iterate, and then the Newton method is used to get the search directions, followed by adaptively choosing the step sizes, which are e.g. the ...