finite difference methods for elliptic equations

Ngày tải lên: 31/03/2014, 15:56

... Finite Difference Methods in Financial Engineering A Partial Differential Equation Approach Daniel J Duffy Finite Difference Methods in Financial Engineering For other titles ... IV 193 FDM FOR MULTIDIMENSIONAL PROBLEMS 18 Finite Difference Schemes for Multidimensional Problems 18.1 Introduction and objectives 18.2 Elliptic equations 18.2.1 A self-adjoint elliptic operator ... Common framework for multi-asset options An overview of finite difference schemes for multi-asset problems Numerical solution of elliptic equations Solving multi-asset Black–Scholes equations Special...

Ngày tải lên: 23/01/2014, 06:20

Ngày tải lên: 23/02/2014, 21:20

Ngày tải lên: 17/03/2014, 12:20

... iterative methods However, domains that span more than free space wavelengths present very difficult computer problems for the method of moments So, for example, modeling a military aircraft for RCS ... dependent approach to solving the Maxwell equations This approach has the advantage that for explicit schemes no matrix inversion is necessary or for compact implicit methods only low dimension sparse ... Maxwell equations in various coordinate systems We also describe the problems which we are going to solve and the methods which we are going to use for each case Chapter is devoted to the formulation...

Ngày tải lên: 17/03/2014, 14:29

... p()/c2 g , (2.125) thus writing that g = 1/g + p(g )/c for some g I (g may be not unique), we have that () for g , and () for g Therefore, the supremum in (2.121) is attained at = g , ... solution for (1.8) is dened to be any possibly discontinuous function U satisfying (1.8) in the sense of distributions, see for example [44], [45] The variable U in which the system takes the form ... conservation laws We say that a convex set U Rp is an invariant domain for (1.8) if it has the property that U (x) U for all x U (t, x) U for all x, t (1.19) Notice that the convexity property is with...

Ngày tải lên: 23/03/2014, 01:20

... article we are filling this gap The mimetic method for the steady diffusion equations (4.1) is too general for the purpose of our theoretical analysis Therefore two simplifications are in order They are ... approaches The next set of difference equations, at cell centers xi+1/2 for i = 2, ,n − 3, takes the form of standard second-order central finite difference discretization for the second derivative To close ... and the nonstandard linear equations in its mathematical formulation The convergence proof gives a possible strategy to obtain similar results for higher order mimetic methods based on the mimetic...

Ngày tải lên: 22/06/2014, 19:20

... Finite Difference Methods in Financial Engineering A Partial Differential Equation Approach Daniel J Duffy Finite Difference Methods in Financial Engineering For other titles ... IV 193 FDM FOR MULTIDIMENSIONAL PROBLEMS 18 Finite Difference Schemes for Multidimensional Problems 18.1 Introduction and objectives 18.2 Elliptic equations 18.2.1 A self-adjoint elliptic operator ... Common framework for multi-asset options An overview of finite difference schemes for multi-asset problems Numerical solution of elliptic equations Solving multi-asset Black–Scholes equations Special...

Ngày tải lên: 27/06/2014, 22:20

... Please refer to [12] for more details Other than finite element method, in this paper, we will discuss an alternative numerical method to handle the equations with distributions For the purpose of ... we will consider numerical methods for solving this kind of differential equations However, the exact solution in hand can be used as benchmark to evaluate numerical methods In the following part, ... 2.2.1 Discrete Singular Convolution Before introducing DSC method, I would like to mention briefly the SINC methods, which is known for many years SINC methods are a family of self-contained...

Ngày tải lên: 27/11/2015, 11:12

... TIME DOMAIN FINITE METHODS FOR SOLUTION OF MAXWELL’S EQUATIONS 2.1 2.2 2.3 2.4 2.5 Maxwell’s Equations Finite Difference Time Domain ... Maxwell’s equations Finite methods are numerical techniques which seek solution of Maxwell’s equations in the differential form The finite methods focused in this thesis are the finite difference ... domain finite methods for the numerical solution of time dependent Maxwell’s equations The two finite methods focused are FDTD and FETD methods The applications of the developed hybrid methods are...

Ngày tải lên: 14/09/2015, 11:39

... complete and put ξ1 := Fully parallel methods for linear PDAEs In this section we study the numerical solution of the following initial boundary value problems (IBVPs) for linear PDAEs: Aut + B∆u = f ... is assumed to be sufficiently smooth We propose two parallel methods for solving the IBVP (5)-(7) where the parallelism will be performed across both the problem and the method According to Proposition ... for the parabolic equation partition of the vector N −1 u(x, 0) such that EN = vt + D∆v = F1 , (9) −1 v(x, 0) = E1 v0 (x), x ∈ Ω (10) v(x, t) = 0, x ∈ ∂Ω, t ∈ (0, 1), (11) and a BVP for the elliptic...

Ngày tải lên: 13/02/2014, 03:20

... in detail the design of efficient explicit methods for non-stiff xiv NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS problems For implicit methods for stiff problems, inexpensive implementation ... Numerical Methods for Ordinary Differential Equations Numerical Methods for Ordinary Differential Equations, Second Edition J C Butcher © 2008 John Wiley & Sons, Ltd ISBN: 978-0-470-72335-7 Numerical Methods ... functions on [0, 1] for which u(0) = u(1) = dx2 The eigenfunctions for the continuous problem are of the form sin(kπx), for 10 NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS k = 1, 2,...

Ngày tải lên: 13/02/2014, 20:20

Ngày tải lên: 17/03/2014, 13:45

... well-posed These include boundary value problems for (stationary) elliptic partial di erential equations and initial-boundary value problems for (time-dependent) equations of parabolic, hyperbolic, and ... Semigroups Parabolic Equations V Implicit Evolution Equations Introduction Regular Equations Pseudoparabolic Equations Degenerate Equations Examples ... of Elliptic Problems Approximation of Evolution Equations Introduction Regular Equations Sobolev Equations Degenerate Equations...

Ngày tải lên: 31/03/2014, 15:56

... non-existence results for quasilinear elliptic equations involving the pLaplacian Boll Unione Mat Ital Scz B 9, 445–484 (2006) Cao, D, Han, P: Solutions for semilinear elliptic equations with critical ... by many authors We refer, e.g., in bounded domains and for p = to [4-6] and for p >1 to [7-11], while in ℝN and for p = to [12,13], and for p >1 to [3,14-17], and the references therein In the ... solutions for p-Laplace elliptic equations involving concave-convex nonlinearities and a Hardytype term Nonlinear Anal 74, 626–638 (2011) doi:10.1016/j.na.2010.09.017 12 Felli, V, Terracini, S: Elliptic...

Ngày tải lên: 20/06/2014, 22:20

... Mikhailov, LG: Elliptic equations with singular coefficients Izv Akad Nauk SSSR, Ser Math 26, 293–312 (1962) (Russian) Achildiyev, SA: First and second boundary value problems for elliptic equations ... elliptic equations, diagonal systems and variational integrals Manuscripta Math 55, 467–486 (1986) doi:10.1007/BF01186659 Rutkauskas, S: On the first boundary value problem for the class of elliptic ... i.e., (6) splits into N separate equations, obviously Let l0 = and, for convenience, only one eigen vector corresponds to this eigenvalue of Λ Then, Re li < for the rest i = 1,p, since the matrix...

Ngày tải lên: 21/06/2014, 00:20

... doi:10.1186/1687-1847-2011-21 Cite this article as: Feng et al.: Some new finite difference inequalities arising in the theory of difference equations Advances in Difference Equations 2011 2011:21 Submit your manuscript ... Theorem 2.1 Feng et al Advances in Difference Equations 2011, 2011:21 http://www.advancesindifferenceequations.com/content/2011/1/21 Page of 17 Theorem 2.5 If for (m, n) Î Ω, u(m, n) satisfies ... v)(u - v) for u ≥ v ≥ 0, where M : Ω × ℝ+ ® ℝ+ p, l are defined as in Theorem 2.1 with p ≥ Feng et al Advances in Difference Equations 2011, 2011:21 http://www.advancesindifferenceequations.com/content/2011/1/21...

Ngày tải lên: 21/06/2014, 02:20

... sufficient conditions for global exponential stability of the impulsive difference equations with distributed delays are obtained The conditions (A1)-(A5) are conservative For example, we get the ... (2010) doi:10.1186/1029-242X-2011-8 Cite this article as: Li et al.: Difference inequality for stability of impulsive difference equations with distributed delays Journal of Inequalities and Applications ... mk-1 + k for k = 2, 3, One can check that all the properties given in (H) are satisfied provided that

Ngày tải lên: 21/06/2014, 03:20

... n,j n,j 27 n,j α2 α3 and < η1 ≤ α1 ≤ θ1 < for all n ∈ N, for all j 1, 2, , N − 1, < ηN ≤ α1 n,j n,j n,N α1 ≤ and ≤ α2 , α3 ≤ θ3 < for all n ∈ N, for all j 1, 2, , N Let {xn }, {un }, {vn ... n,j and < η1 ≤ α1 ≤ θ1 < for all n ∈ N, for all j 1, 2, , N − 1, < ηN ≤ αn,N ≤ and 28 Fixed Point Theory and Applications n,j n,j ≤ α2 , α3 ≤ θ3 < for all n ∈ N, for all j generated by x1 ... 2.8 for all x ∈ C Lemma 2.7 see Assume that F : C × C → R satisfies (A1)–(A4) For r > and x ∈ H, define a mapping Tr : H → C as follows: Tr x z ∈ C : F z, y y − z, z − x ≥ 0, ∀y ∈ C r 2.9 for...

Ngày tải lên: 21/06/2014, 11:20

... regularized long wave equations, ” Journal of Partial Differential Equations, vol 15, no 1, pp 35–45, 2002 17 Y D Shang and B Guo, “Global attractors for a periodic initial value problem for dissipative ... restraint operator for the SRLWEs and proved its stability and obtained the optimum error estimates There are other methods such as pseudospectral method, finite difference method for the initial-boundary ... L2 ≤ C It is followed from Sobolev inequality that u L∞ ≤ C Finite Difference Scheme and Its Error Estimation Let h and τ be the uniform step size in the spatial and temporal direction, respectively...

Ngày tải lên: 21/06/2014, 11:20