multiscale phenomena green s functions the dirichlet to neumann formulation subgrid scale models bubbles and the origins of stabilized methods abstract an approach is developed for deriving variational methods capable of representing multiscale phenomena the ideas are first illustrated on the exterior problem for the helmholtz equation this leads to the well known dirichlet to neumann formulation next a class of subgrid scale models is developed and the relationships to bubble function methods and stabilized methods are established it is shown that both the latter methods are approximate subgrid scale models the identification for stabilized methods leads to an analytical formula for the intrinsic time scale whose origins have been a mystery heretofore

a stabilized meshfree reproducing kernel based method for convection diffusion problems in this paper we develop a meshfree particle based method for convection diffusion problems discretization is performed by using piecewise constant kernels the stabilized scheme is based on a new upwind kernel we show that accurate and stable scheme can be obtained by using purpose built kernels it also shown that under some conditions the classical optimal finite difference scheme can be derived by the new method several numerical tests validate the method copyright 2011 john wiley sons ltd

on triangular norm based propositional fuzzy logics abstract fuzzy logics based on triangular norms and their corresponding conorms are investigated an affirmative answer to the question whether in such logics a specific level of satisfiability of a set of formulas can be characterized by the same level of satisfiability of its finite subsets is given tautologies contradictions and contigencies with respect to such fuzzy logics are studied in particular for the important cases of min max and ukasiewicz logics finally fundamental t norm based fuzzy logics are shown to provide a gradual transition between min max and ukasiewicz logics

far field boundary conditions for black scholes equations in this paper we consider the partial differential equations approach for valuing european style options in order to solve the equations numerically by finite difference or finite element methods it is necessary to introduce an artificial boundary in order to make the computational domain bounded we derive pointwise bounds for the error caused by various boundary conditions imposed on the artificial boundary the error estimates can be used to determine a priori a suitable location for the artificial boundary in terms of a given error tolerance

the variational multiscale method a paradigm for computational mechanics abstract we present a general treatment of the variational multiscale method in the context of an abstract dirichlet problem we show how the exact theory represents a paradigm for subgrid scale models and a posteriori error estimation we examine hierarchical p methods and bubbles in order to understand and ultimately approximate the fine scale green s function which appears in the theory we review relationships between residual free bubbles element green s functions and stabilized methods these suggest the applicability of the methodology to physically interesting problems in fluid mechanics acoustics and electromagnetics

computing american option price under regime switching with rationality parameter american put option pricing under regime switching is modelled by a system of coupled partial differential equations the proposed model combines better the reality of the market by incorporating the regime switching jointly with the emotional behaviour of traders using the rationality parameter approach recently introduced by tagholt gad and lund petersen to cope with possible irrational exercise policy the classical rational exercise is recovered as a limit case of the rational parameter the resulting nonlinear system of pdes is solved by a weighted finite difference method also known as method in order to avoid the need of an iterative method for nonlinear system the term with rationality parameter and the coupling term are treated explicitly next the resulting linear system is solved by thomas algorithm stability conditions for the numerical scheme are studied by using von neumann approach numerical examples illustrate the efficiency and accuracy of the proposed method

a fast high order finite difference algorithm for pricing american options we describe an improvement of han and wu s algorithm h han x wu a fast numerical method for the black scholes equation of american options siam j numer anal 41 6 2003 2081 2095 for american options a high order optimal compact scheme is used to discretise the transformed black scholes pde under a singularity separating framework a more accurate free boundary location based on the smooth pasting condition and the use of a non uniform grid with a modified tridiagonal solver lead to an efficient implementation of the free boundary value problem extensive numerical experiments show that the new finite difference algorithm converges rapidly and numerical solutions with good accuracy are obtained comparisons with some recently proposed methods for the american options problem are carried out to show the advantage of our numerical method

multiary α resolution principle for a lattice valued logic this paper focuses on resolution based automated reasoning theory in a lattice valued logic system with truth values that are defined in a lattice valued logical algebraic structure lattice implication algebras lias which essentially aims to extend the classical logic to handle automated deduction under an uncertain environment concretely we investigate a generalization of the known conjunctive normal form cnf in the classical logic representation that we call the generalized conjunctive normal form gcnf which aims to characterize the constants and implication connectives that are essentially different from the ones in classical logic we then extend the established resolution principle at a certain truth value level called resolution in this lattice valued logic to a more general form i e from binary resolution to multiary resolution the extension to multiary resolution starts from lattice valued propositional logic lp x while its theorems of both soundness and completeness are proved multiary resolution principle is then further established in the corresponding lattice valued first order logic lf x along with its soundness theorem lifting lemma and completeness theorem meanwhile an important result that multiary resolution principle in lf x can be equivalently transformed into that in lp x to some extent is obtained all these works will theoretically support the establishment of an automated reasoning algorithm and its implementation with further applications into automated deduction and decision making problems under uncertainty

a fast numerical method for the black scholes equation of american options this paper introduces a fast numerical method for computing american option pricing problems governed by the black scholes equation the treatment of the free boundary is based on some properties of the solution of the black scholes equation an artificial boundary condition is also used at the other end of the domain the finite difference method is used to solve the resulting problem computational results are given for some american call option problems the results show that the new treatment is very efficient and gives better accuracy than the normal finite difference method

graded many valued resolution with aggregation abstract the aim of this paper is to give a sound resolution deduction rule in many valued logic with truth value range 0 1 and with arbitrary connectives and graded information we introduce and study the resolution truth function which will evaluate the truth value of the result of resolution conditions under which this function yields an aggregation operator will be given

a petrov galerkin finite element method for convection dominated flows an accurate upwinding technique for satisfying the maximum principle abstract in this paper we present a new petrov galerkin method for convection dominated flow problems which is conservative and satisfies the discrete maximum principle this method also possesses no spurious crosswind diffusion and gives very accurate solutions the method is representative of a class of methods which may be described as fixed mesh adaptive

non smooth kernels for meshfree methods in fluid dynamics a function and its first two derivatives are estimated by convolutions with well chosen non differentiable kernels the convolutions are in turn approximated by newton cotes integration techniques with the aid of a polynomial interpolation based on an arbitrary finite set of points precise numerical results are obtained with far fewer points than that in classic sph and error bounds are derived

finite difference methods for pricing american put option with rationality parameter numerical analysis and computing abstract in this paper finite difference methods for pricing american option with rationality parameter are proposed the irrational exercise policy arising in american options is characterized in terms of a rationality parameter the model is formulated in terms of a new nonlinear black scholes equation that requires specific numerical methods although the solution converges to the solution of the classical american option price when the parameter tends to infinity for finite values of the parameter the classical boundary conditions cannot apply and we propose specific ones a logarithmic transformation is used to improve properties of the numerical solution that is constructed by explicit finite difference method numerical analysis provides stability conditions for the methods and its positivity properties of intensity function are studied from the point of view of numerical solution concerning the numerical methods for the original problem we propose the method for time discretization thus including explicit fully implicit and crank nicolson schemes as particular cases the nonlinear term is treated by a newton method the convergence rate is illustrated by numerical examples

constructing positive reliable numerical solution for american call options a new front fixing transformation is applied to the black scholes equation for the american call option pricing problem the transformed non linear problem involves homogeneous boundary conditions independent of the free boundary the numerical solution by an explicit finite difference method is positive and monotone stability and consistency of the scheme are studied the explicit proposed method is compared with other competitive implicit ones from the points of view accuracy and computational cost

a mixed hybrid finite element method for convection diffusion problems a mixed hybrid finite element method for scalar diffusion convection problems is presented in this method the lowest degree raviart thomas finite element is used for the diffusive term the convective term is treated by means of a lagrange multiplier which is introduced in the hybrid form the numerical results show that this method produces very accurate solutions for high peclet numbers

filter based resolution principle for lattice valued propositional logic lp x as one of most powerful approaches in automated reasoning resolution principle has been introduced to non classical logics such as many valued logic however most of the existing works are limited to the chain type truth value fields lattice valued logic is a kind of important non classical logic which can be applied to describe and handle incomparability by the incomparable elements in its truth value field in this paper a filter based resolution principle for the lattice valued propositional logic lp x based on lattice implication algebra is presented where filter of the truth value field being a lattice implication algebra is taken as the criterion for measuring the satisfiability of a lattice valued logical formula the notions and properties of lattice implication algebra filter of lattice implication algebra and the lattice valued propositional logic lp x are given firstly the definitions and structures of two kinds of lattice valued logical formulae i e the simple generalized clauses and complex generalized clauses are presented then finally the filter based resolution principle is given and after that the soundness theorem and weak completeness theorems for the presented approach are proved

conditional full stability of positivity preserving finite difference scheme for diffusion advection reaction models this work has been partially supported by the ministerio de economia y competitividad spanish grant mtm2017 89664 p

resolution and model building in the infinite valued calculus of lukasiewicz abstract we discuss resolution and its complexity in the infinite valued sentential calculus of l ukasiewicz with special emphasis on model building algorithms for satisfiable sets of clauses we prove that resolution and model building are polynomially tractable in the fragments given by horn clauses and by krom clauses i e clauses with at most two literals generalizing the pre existing literature on resolution in infinite valued logic by a positive literal we mean a negationless formula in one variable built only from the connectives we prove that the expressive power of our literals encompasses all monotone mcnaughton functions of one variable

convergence analysis of finite element method for a parabolic obstacle problem abstract a conforming finite element method is proposed and analyzed for numerical approximation of the solution of a parabolic variational inequality of the obstacle problem the model problem which is originally proposed using a general obstacle is reframed as a model problem with zero obstacle but with non homogeneous dirichlet boundary conditions subsequently the discrete problem is reframed and the error analysis proving the convergence of the method is performed the analysis requires a positive preserving interpolation with non homogeneous dirichlet boundary condition and a post processed solution that satisfies the boundary conditions sharply the results in the article extend the results of johnson sinum 1976 for a zero obstacle function to a more general obstacle function

quadratic convergence for valuing american options using a penalty method the convergence of a penalty method for solving the discrete regularized american option valuation problem is studied sufficient conditions are derived which both guarantee convergence of the nonlinear penalty iteration and ensure that the iterates converge monotonically to the solution these conditions also ensure that the solution of the penalty problem is an approximate solution to the discrete linear complementarity problem the efficiency and quality of solutions obtained using the implicit penalty method are compared with those produced with the commonly used technique of handling the american constraint explicitly convergence rates are studied as the timestep and mesh size tend to zero it is observed that an implicit treatment of the american constraint does not converge quadratically as the timestep is reduced if constant timesteps are used a timestep selector is suggested which restores quadratic convergence

streamline upwind petrov galerkin formulations for convection dominated flows with particular emphasis on the incompressible navier stokes equations abstract a new finite element formulation for convection dominated flows is developed the basis of the formulation is the streamline upwind concept which provides an accurate multidimensional generalization of optimal one dimensional upwind schemes when implemented as a consistent petrov galerkin weighted residual method it is shown that the new formulation is not subject to the artificial diffusion criticisms associated with many classical upwind methods the accuracy of the streamline upwind petrov galerkin formulation for the linear advection diffusion equation is demonstrated on several numerical examples the formulation is extended to the incompressible navier stokes equations an efficient implicit pressure explicit velocity transient algorithm is developed which accomodates several treatments of the incompressibility constraint and allows for multiple iterations within a time step the effectiveness of the algorithm is demonstrated on the problem of vortex shedding from a circular cylinder at a reynolds number of 100