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141.
Tatiana Chernogorova Radoslav Valkov 《Numerical Methods for Partial Differential Equations》2015,31(3):822-846
We consider the locally one‐dimensional backward Euler splitting method to solve numerically the Hull and White problem for pricing European options with stochastic volatility in the presence of a mixed derivative term. We prove the first‐order convergence of the time‐splitting. The parabolic equation degenerates on the boundary x = 0 and we apply a fitted finite volume scheme to the equation to resolve the degeneracy and derive the fully discrete problem as we also investigate the discrete maximum principle. Numerical experiments illustrate the efficiency of our difference scheme. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 822–846, 2015 相似文献
142.
Interpolating minimal energy C1‐Surfaces on Powell–Sabin Triangulations: Application to the resolution of elliptic problems 下载免费PDF全文
M. A. Fortes P. González M. J. Ibáñez M. Pasadas 《Numerical Methods for Partial Differential Equations》2015,31(3):798-821
In this article, we present a method to obtain a C1‐surface, defined on a bounded polygonal domain Ω, which interpolates a specific dataset and minimizes a certain “energy functional.” The minimization space chosen is the one associated to the Powell–Sabin finite element, whose elements are C1‐quadratic splines. We develop a general theoretical framework for that, and we consider two main applications of the theory. For both of them, we give convergence results, and we present some numerical and graphical examples. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 798–821, 2015 相似文献
143.
Peter Albers Monika Maier Martin Reisinger Bernd Hannebauer Rudolf Weinand 《Crystal Research and Technology》2015,50(11):846-865
The structural properties of finely divided inorganic materials such as metal and metalloid oxides, silicates or carbonates of both synthetic and natural origin are compared by means of electron microscopy and tomography. The structure of the outer surfaces of various compact or compacted agglomerates may suggest some striking similarities between various amorphous silica on the one hand and crystalline titania and alumina on the other however the details of the interior fine structure are completely different. Inside of the crystalline aggregates of, for example, alumina and titania distinct grain boundaries between the inter‐grown primary crystallites exist. Also physical boundaries between different solid phases and crystalline/amorphous transitions in core/shell structures can occur. No physical grain or phase boundaries were found inside of synthetic amorphous silica or para‐crystalline carbon black thus, the aggregate is the constituent particle. Synthetic amorphous silica from different production technologies (fumed/pyrogenic, precipitated, aerogel, gel) may exhibit different macro‐morphology but distinct similarities of the amorphous silica networks. Computational studies on silica and titania underline the stability of constituent particles and aggregates as observed by means of TEM after dispersing the original materials by ultra‐sonication. 相似文献
144.
145.
A PIECEWISE–LINEARIZED METHOD FOR ORDINARY DIFFERENTIAL EQUATIONS: TWO–POINT BOUNDARY–VALUE PROBLEMS
Piecewise-linearized methods for the solution of two-point boundary value problems in ordinary differential equations are presented. These problems are approximated by piecewise linear ones which have analytical solutions and reduced to finding the slope of the solution at the left boundary so that the boundary conditions at the right end of the interval are satisfied. This results in a rather complex system of non-linear algebraic equations which may be reduced to a single non-linear equation whose unknown is the slope of the solution at the left boundary of the interval and whose solution may be obtained by means of the Newton–Raphson method. This is equivalent to solving the boundary value problem as an initial value one using the piecewise-linearized technique and a shooting method. It is shown that for problems characterized by a linear operator a technique based on the superposition principle and the piecewise-linearized method may be employed. For these problems the accuracy of piecewise-linearized methods is of second order. It is also shown that for linear problems the accuracy of the piecewise-linearized method is superior to that of fourth-order-accurate techniques. For the linear singular perturbation problems considered in this paper the accuracy of global piecewise linearizat ion is higher than that of finite difference and finite element methods. For non-linear problems the accuracy of piecewise-linearized methods is in most cases lower than that of fourth-order methods but comparable with that of second-order techniques owing to the linearization of the non-linear terms. 相似文献
146.
147.
周富军 《高校应用数学学报(英文版)》2006,21(2):143-151
§1Introduction Avarietyofpartialdifferentialequationmodelsfortumorgrowthortherapyhave beendevelopedinthelastthreedecades[see2,3,16-18,21-26].Mostofthosemodelsare informoffreeboundaryproblems,andareverydiversified.Rigorousmathematical analysisofsuchfreeboundaryproblemshasdrawngreatinterest,andmanyinteresting resultshavebeenestablished[4-15].Inthispaperwedealwithamathematicalmodeldescribingtumorchemotherapy.In thismodelthetumorisviewedasdenselypacked,radially-symmetricsphereofradiusR(t)contain… 相似文献
148.
The influence of the location of the outflow computational boundary on the unsteady incompressible flow past a circular cylinder at Reynolds number 100 is examined. The vorticity-streamfunction formulation of the Navier-Stokes equations is used in all computations. Two types of outflow boundary conditions are subjected to a series of tests in which the domain length is gradually reduced. The traction-free condition performs well in most cases and allows the outflow boundary to be located as close as 6.5 cylinder diameters from the body. The other boundary condition type is not as forgiving, but has the advantage of being simpler to implement and can still provide reasonably accurate solutions. It is also observed that both condition types can influence the flow field strongly and globally when the boundary is brought closer than 2.5 diameters from the body. In such cases the temporal periodicity of the solution is lost. 相似文献
149.
Titanium is a commonly used material in aviation, aerospace, and military applications, due to the outstanding mechanical properties of titanium and its alloys. However, its relatively low thermal conductivity restricts its extended usage. The use of graphene as a filler shows great potential for the enhancement of thermal conductivity in titanium-based metal-matrix composites (MMCs). We used classical molecular dynamics (MD) simulation methods to explore the thermal conductance at the titanium–graphene (Ti/Gr) interface for its thermal boundary conductance, which plays an important role in the thermal properties of Ti-based MMCs. The effects of system size, layer number, temperature, and strain were considered. The results show that the thermal boundary conductance (TBC) decreases with an increasing layer number and reaches a plateau at n = 5. TBC falls under tensile strain and, in turn, it grows with compressive strain. The variation of TBC is explained qualitatively by the interfacial atomic vibration coupling factor. Our findings also provide insights into ways to optimize future thermal management based on Ti-based MMCs materials. 相似文献
150.
Flow physics of transvalvular flows in the aorta with bioprosthetic valves are investigated using computational modelling. For the efficient simulations of flow-structure-interaction in transvalvular flows, a simplified, reduced degree of freedom valve model is employed with a sharp interface immersed boundary based incompressible flow solver. Simulations are performed for normal as well as abnormal valves with reduced leaflet motion that models the effect of early leaflet thrombosis. The structure of the aortic jet and the hemodynamic stresses on the aortic wall are analysed to understand the hemodynamic impacts and possible long-term clinical implications of sub-clinical, reduced leaflet motion. The simulation results have shown that the reduced leaflet motion tilts the direction of aortic jet and generates stronger flow separation and re-attachment on the aortic wall downstream from the reduced motion leaflets. The modified flow pattern increases the wall pressure fluctuation and average wall shear stress on the downstream aortic wall, and results in the asymmetric oscillatory shear index distributions, which may have long-term clinical implications such as aortic wall damage and remodelling. 相似文献