nonlinear superposition formulae of integrable partial differential equations by the singular manifold method
partial differential equations and the finite element method - pave1 solin
Ngày tải lên :
31/03/2014, 15:57
... list of the titles in this series appears at the end of this volume Partial Differential Equations and the Finite Element Method Pave1 Solin The University of Texas at El Paso Academy of Sciences ... during the two years of my work on the manuscript P The author acknowledges the support of the Czech Science Foundation under the Grant No 102/05/0629 xxvii Partial Differential Equations and the ... of the reentrant comer 450 B.14 Computational domain of the cone-sphere problem 45 B.15 Approximate solution p)t,p the cone-sphere problem of 452 B.16 Details of the singularity of 452 B.17 The...
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Synthesis and photoluminescence property of silicon carbon nanowires synthesized by the thermal evaporation method
Ngày tải lên :
16/03/2014, 15:21
... [23] of SiC, the emission peak for b-SiC nanowires is obviously shifted to the blue The emergence of the peak with a blueshift is due to the existence of oxygen defects in the amorphous layer, the ... directly because of using AAO template, and the template made the concentration of the SiO vapor increase Thus, overgrowth of the nanowires became possible by using AAO template The X-ray diffraction ... The SiO2 sheath could be easily removed by etching in hydrofluoric acid (HF) The thickness of the SiO2 sheath could be controlled by changing the etching time Fig also shows that the spacing of...
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Tài liệu Báo cáo " Fully parallel methods for a class of linear partial differential-algebraic equations " pptx
Ngày tải lên :
13/02/2014, 03:20
... Proof Thanks to the nonnegativity of the pencil {A, B}, we can split the IBVP (5)-(7) into the IBVP (9)-(11) and the BVP (12)-(13) Theorems 4.11 and 5.2 [4] ensure that the PFS method in the ... what follows, we study the relation between the total (CPU) time spent on the performance of a program, the speedup and the efficiency of this performance The speedup of the performance is defined ... nodes of 51.2GFlops Each node contains two Intel Xeon dual core 3.2GHz, 2GB Ram The following table shows the dependence of the error of the approximate solutions on the τ number N = h while the...
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Báo cáo y học: "Modelling of oedemous limbs and venous ulcers using partial differential equations" pdf
Ngày tải lên :
13/08/2014, 23:20
... generated form offunctionin 3-space TheThethe of a surfaceare all takenby the fourth order PDE Figure conditions defined in the to be curves conditions The shape of a surface generated by the fourth ... manipulation tool in that the shape of the surface closely follows the shape of the boundary conditions tionsshape of a surface generated by the fourth both PDE where thederivatives (a) The boundary conditions ... http://www.tbiomed.com/content/2/1/28 where the conditions the all taken tothe in 3-space(a) The The shape of a surfaceare form of curves sixth order PDE Figure conditions defined in generated by be positions The shape of a surface...
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Partial Differential Equations part 1
Ngày tải lên :
28/10/2013, 22:15
... are: • What are the variables? • What equations are satisfied in the interior of the region of interest? • What equations are satisfied by points on the boundary of the region of interest? (Here ... conditions) govern the evolution in time of points on the boundary of the spatial region of interest? Examples: Dirichlet conditions specify the values of the boundary points as a function of time; Neumann ... “simultaneously,” these problems usually boil down, at least conceptually, to the solution of large numbers of simultaneous algebraic equations When such equations are nonlinear, they are usually solved by...
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Partial Differential Equations part 2
Ngày tải lên :
07/11/2013, 19:15
... series and includes the nonlinearity of the equations explicitly There is an analytic solution for the evolution of two uniform states of a fluid separated by a discontinuity, the Riemann shock ... approximate the fluid by a large number of cells of uniform states, and piece them together using the Riemann solution There have been many generalizations of Godunov’s approach, of which the most ... careful methods We accordingly adopt it exclusively (See, for example, [1] for a discussion of other methods of stability analysis.) Lax Method The instability in the FTCS method can be cured by a...
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Tài liệu Partial Differential Equations part 3 pptx
Ngày tải lên :
15/12/2013, 04:15
... 19 Partial Differential Equations The physical interpretation of the restriction (19.2.6) is that the maximum allowed timestep is, up to a numerical factor, the diffusion time across a cell of ... methods Here, on the other hand, is how one gets to the second of our above philosophical answers, combining the stability of an implicit method with the accuracy of a method that is second-order ... nasty set of coupled nonlinear equations to solve at each timestep Often there is an easier way: If the form of D(u) allows us to integrate dz = D(u)du (19.2.23) analytically for z(u), then the right-hand...
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Tài liệu Partial Differential Equations part 4 ppt
Ngày tải lên :
15/12/2013, 04:15
... increase the order of a differencing method to greater than the order of the original PDEs, you introduce spurious solutions to the difference equations This does not create a problem if they all ... un+1 j,l (19.3.16) The advantage of this method is that each substep requires only the solution of a simple tridiagonal system Operator Splitting Methods Generally The basic idea of operator splitting, ... scheme for the operator L In fact, as a rule of thumb, it is often sufficient to have stable Ui ’s only for the operator pieces having the highest number of spatial derivatives — the other Ui ’s...
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Tài liệu Partial Differential Equations part 5 ppt
Ngày tải lên :
15/12/2013, 04:15
... level of CR, we have reduced the number of equations by a factor of two Since the resulting equations are of the same form as the original equation, we can repeat the process Taking the number of ... space The cyclic reduction method is somewhat more general; its applicability is related to the question of whether the equations are separable (in the sense of “separation of variables”) Both methods ... dimension and solve the tridiagonal equations by the usual algorithm in the other dimension) gives about a factor of two gain in speed The optimal FACR with r = gives another factor of two gain in...
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Tài liệu Partial Differential Equations part 6 doc
Ngày tải lên :
15/12/2013, 04:15
... modulus < for the relaxation to work at all! The rate of convergence of the method is set by the rate for the slowest-decaying eigenmode, i.e., the factor with largest modulus The modulus of this largest ... is the diagonal part of A, L is the lower triangle of A with zeros on the diagonal, and U is the upper triangle of A with zeros on the diagonal In the Jacobi method we write for the rth step of ... Gauss-Seidel method • If ρJacobi is the spectral radius of the Jacobi iteration (so that the square of it is the spectral radius of the Gauss-Seidel iteration), then the optimal choice for ω is given by...
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Tài liệu Partial Differential Equations part 7 doc
Ngày tải lên :
24/12/2013, 12:16
... Chapter 19 Partial Differential Equations From One-Grid, through Two-Grid, to Multigrid The key idea of the multigrid method can be understood by considering the simplest case of a two-grid method ... relaxation methods reduce the amplitude of the nonsmooth components by large factors on each iteration: They are good smoothing operators For the two-grid iteration, on the other hand, components of the ... you increase the number of cycles per level The asymptotic value of the solution is the exact solution of the difference equations The difference between this exact solution and the solution...
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Functional analysis sobolev spaces and partial differential equations
Ngày tải lên :
04/02/2014, 11:10
... mention also the proof of the existence of the Green’s function for the Laplacian by the method of P Lax; see P Lax [1] (Section 9.5) and P Garabedian [1] The proof of the existence of a solution ... proof of the Krein–Milman theorem, see Problem (b) In the theory of partial differential equations Let us mention, for example, that the existence of a fundamental solution for a general differential ... are often fascinated by the most abstract constructions in mathematics are usually attracted by the elegance of FA On the other hand, they are repelled by the neverending PDE formulas with their...
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Tài liệu AN INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS ppt
Ngày tải lên :
16/02/2014, 15:20
... 2.3 The method of characteristics We solve first-order PDEs by the method of characteristics This method was developed in the middle of the nineteenth century by Hamilton Hamilton investigated the ... Chapter r The order of an equation The first classification is according to the order of the equation The order is defined to be the order of the highest derivative in the equation If the highest ... slope of the projection of 2.4 Examples of the characteristics method 33 y projection of Γ char x Figure 2.3 The characteristics and projection of for Example 2.5 the initial curve there Namely, the...
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Tài liệu Boundary Value Problems, Sixth Edition: and Partial Differential Equations pptx
Ngày tải lên :
17/02/2014, 14:20
... interval of interest is a singular point of the differential equation In the other, the interval is infinitely long Regular Singular Point Recall that a point x0 is a (regular) singular point of the differential ... exponentials The contribution of each root or pair of conjugate roots of Eq (28) is summarized in Table Since the sum of the multiplicities of the roots of Eq (28) is n, the sum of the contributions produces ... moving Then by Newton’s second law, the sum of the horizontal components of the forces on the segment is 0, and likewise for the vertical components If T(x) and T(x+ x) are the magnitudes of the...
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Partial Differential Equations and Fluid Mechanics doc
Ngày tải lên :
14/03/2014, 10:20
... concerning the effect of the material parameters on the nature of these solutions The structure of the paper is the following In the next section, we formulate the governing equations, and state the ... fluids Bridges & Rajagopal (2006) associate the concentration with the ratio of the density of the reactant to the sum of the density of the reactant and the homogeneous fluid While a concentration ... the fluid obtained by “homogenizing” the multi-constituent fluid such as blood) are of comparable density, then assigning the notion of the ratio of the density of the reactant to the total density...
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Entropy and partial differential equations evans l c
Ngày tải lên :
17/03/2014, 14:29
... conservation of energy: The work done by the fluid along any cycle equals the heat gained by the fluid along the cycle Remark We assume in (9) that the units of work and heat are the same If not, ... and furthermore that for the range of values we consider (11) the “inf” in each of (7), (8), (9) is attained at a unique point in the domain of E We can then recast the definitions (7)–(9): Thermodynamic ... there has been no heat loss or gain, EC = EA + EB This is a form of the First Law of thermodynamics We however not write a similar equality for the entropy S Rather we invoke the Second Law of...
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harmonic analysis and partial differential equations - b. dahlberg, c. kenig
Ngày tải lên :
31/03/2014, 15:16
... Theorem 1.2 19 Proof of Theorem 1.6 25 Proof of Theorem 1.3 37 Proof of Theorem 1.4 47 Dirichlet Problem for Lipschitz domains The nal arguments for the L2-theory 51 Existence of solutions to Dirichlet ... v(x) where v Lp(Rn): For the proof of the existence of non-tangential limits of py u0 we refer to e.g Stein/Weiss 2] The notion of solution of the Dirichlet problem and any other problem, is sound ... is done by a theorem of Daivd and Journ 3] Theorem 1.6 T bounded on L2 i T BMO The de nition of BMO and the theorem and its proof will be discussed in Chapter References 1] E M Stein: Singular...
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hilbert space methods for partial differential equations - r. showalter
Ngày tải lên :
31/03/2014, 15:56
... if it depends only on the mean value of each ' This observation is the key to the proof of our next result Theorem 1.5 (a) If S is a distribution on R, then there exists another distribution T ... determined as the th partial derivative of f in the sense of distribution on G These remarks prove the following characterization Theorem 2.1 Let G be open in Rn and m Then f H m(G) if and only if there ... be the identity, where = (0 : : : 0), so C (G) = C (G) (e) For f C (G), the support of f is the closure in G of the set fx G : f (x) 6= 0g and we denote it by supp(f ) C0 (G) is the subset of...
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introduction to partial differential equations - a computational approach - a. tveito, r. winther
Ngày tải lên :
31/03/2014, 15:56
... naturally in the analysis of the Cauchy problem for the heat equation In the context of differential equations the function S is therefore frequently referred to as the Gaussian kernel function or the ... Similarly, a singular matrix can be characterized by the following equivalent statements: • The matrix A is singular • The determinant of A is zero • The vectors defined by the rows of A form a ... solves the Cauchy problem for any c > However, the solution of the problem (1.48)–(1.49) is unique Uniqueness of the solution of the heat equation will be discussed later in the text But then,...
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