partial differential equation toolbox in matlab

Ngày tải lên: 08/04/2014, 10:27

... Subscribing user registration service@mathworks.com Order status, license renewals, passcodes info@mathworks.com Sales, pricing, and general information Partial Differential Equation Toolbox ... called nonlinear and FEM yields a nonlinear system K(U) U= F(U). You can use iterative methods for solving the nonlinear system. The toolbox provides a nonlinear solver called pdenonlin using a ... of points inside and on a circle. ãPolygon object represents the set of points inside and on a polygon given by a set of line segments. ãRectangle object represents the set of points inside...

Ngày tải lên: 26/01/2014, 02:20

Ngày tải lên: 28/04/2014, 10:17

Ngày tải lên: 22/06/2014, 21:20

... IL5 – the interleukin 5 gene, λ Ig – the λ -chain of immunoglobulin gene, γIg – the γ-chain of immunoglobulin gene, IFN-ind – the interferone-inducible gene 6-16, IL4R – the interleukin 4 receptor ... effects of calpains in cancer cells [27-29] suggest that calpain participates in cell malignization by digesting the p53 tumor suppressor. Besides, calpains participate in induction of HIV ... of immunoglobulin gene; IFN-ind: the interferon-inducible gene 6-16; IL4R: the interleukin 4 receptor gene; TAP2: the transport protein gene; hnRNP A1: the human ribonucleoprotein А1 gene; SMG-1...

Ngày tải lên: 02/11/2012, 11:08

... unitize a quaternion Kinematics diff2tr differential motion vector to transform fkine compute forward kinematics ikine compute inverse kinematics ikine560 compute inverse kinematics for Puma 560 ... 1 A i cosθ i sinθ i cosα i sinθ i sinα i a i cosθ i sinθ i cosθ i cosα i cosθ i sinα i a i sinθ i 0 sinα i cosα i d i 0 0 0 1 represents each link’s coordinate frame with respect to the previous link’s ... giving joint motion in terms of input torques. Walker and Orin[23] describe several methods for computing the forward dynamics, and all make use of an existing inverse dynamics solution. Using...

Ngày tải lên: 19/10/2013, 18:15

... America). Chapter 19. Partial Differential Equations 19.0 Introduction The numerical treatment of partial differential equations is, by itself, a vast subject. Partial differential equations are at ... Numerical Recipes dealing with partial differential equations alone. (The references [1-4] provide, of course, available alternatives.) In most mathematics books, partial differential equations (PDEs) ... and (19.0.2) both define initial value or Cauchy problems: If information on u (perhaps including time derivative information) is 827 830 Chapter 19. Partial Differential Equations Sample page...

Ngày tải lên: 28/10/2013, 22:15

... various ways of improving the accuracy of first-order upwind differencing. In the continuum equation, material originally a distance v∆t away 840 Chapter 19. Partial Differential Equations Sample ... own domain of dependency determined by the choice of points on one time slice (shown as connected solid dots) whose values are used in determining a new point (shown connected by dashed lines). ... viscosity to the equations, modeling the way Nature uses real viscosity to smooth discontinuities. A good starting point for trying out this method is the differencing scheme in §12.11 of [1] ....

Ngày tải lên: 07/11/2013, 19:15

... form again and in practice usually retains the stability advantages of fully implicit differencing. Schr ă odinger Equation Sometimes the physical problem being solved imposes constraints on ... accurate in time for the scales that we are interested in. The second answer is to let small-scale features maintain their initial amplitudes, so that the evolution of the larger-scale features of interest ... steps of the other kind, to drive the small-scale stuff into equilibrium. Let us now see where these distinct differencing schemes come from: Consider the following differencing of (19.2.3), u n+1 j −...

Ngày tải lên: 15/12/2013, 04:15

... underlying PDEs, perhaps allowing second-order spatial differencing for first-order -in- space PDEs. When you increase the order of a differencing method to greater than the order of the original ... ξ n e ik x j∆ e ik y l∆ (19.3.5) Substituting in equation (19.3.3), we find ξ = 1 2 (cos k x ∆+cosk y ∆)− iα x sin k x ∆ − iα y sin k y ∆(19.3.6) where α x = v x ∆t ∆ ,α y = v y ∆t ∆ (19.3.7) 19.3 Initial Value Problems in Multidimensions 853 Sample ... 100 mesh points requires at least 100 times as much computing. You generally have to be content with very modest spatial resolution in multidimensional problems. Indulge us in offering a bit of...

Ngày tải lên: 15/12/2013, 04:15

... 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 mesh points to be a power ... get the y-values on these x-lines. Then fill in the intermediate x-lines as in the original CR algorithm. The trick is to choose the number of levels of CR so as to minimize the total number of ... mentioned in Đ19.0, relaxation methods involve splitting the sparse matrix that arises from finite differencing and then iterating until a solution is found. There is another way of thinking about...

Ngày tải lên: 15/12/2013, 04:15

... become available. In other words, the averaging is done in place” instead of being “copied” from an earlier timestep to a later one. If we are proceeding along the rows, incrementing j for fixed ... mentioned in Đ19.0, relaxation methods involve splitting the sparse matrix that arises from finite differencing and then iterating until a solution is found. There is another way of thinking about ... get the y-values on these x-lines. Then fill in the intermediate x-lines as in the original CR algorithm. The trick is to choose the number of levels of CR so as to minimize the total number of...

Ngày tải lên: 15/12/2013, 04:15

... residual.#define NGMAX 15 void mgfas(double **u, int n, int maxcyc) Full Multigrid Algorithm for FAS solution of nonlinear elliptic equation, here equation (19.6.44). On input u[1 n][1 n] contains the ... com- puted.#define NGMAX 15 void mglin(double **u, int n, int ncycle) Full Multigrid Algorithm for solution of linear elliptic equation, here the model problem (19.0.6). On input u[1 n][1 n] contains the ...  1 3 τ h  1 3 τ h (19.6.39) The stopping criterion is thus equation (19.6.36) with  = ατ h ,α∼ 1 3 (19.6.40) We have one remaining task before implementing our nonlinear multigrid algorithm: choosing a nonlinear relaxation...

Ngày tải lên: 24/12/2013, 12:16

... unitize a quaternion Kinematics diff2tr differential motion vector to transform fkine compute forward kinematics ikine compute inverse kinematics ikine560 compute inverse kinematics for Puma 560 ... 1 A i cosθ i sinθ i cosα i sinθ i sinα i a i cosθ i sinθ i cosθ i cosα i cosθ i sinα i a i sinθ i 0 sinα i cosα i d i 0 0 0 1 represents each link’s coordinate frame with respect to the previous link’s ... provided joint coordinates prior to any kinematic or dynamic operation, subtracted after inverse kinematics. 3. Greatly improved the plot function, adding 3D cylinders and markers to indicate joints,...

Ngày tải lên: 19/01/2014, 17:20

... occur in a wide range of questions, in both pure and applied mathematics. They appear in linear and nonlinear PDEs that arise, for example, in differential geometry, harmonic analysis, engineering, ... Recall that in general, a pointwise limit of continuous maps need not be continuous. The linearity assumption plays an essential role in Theorem 2.2. Note, however, that in the setting of Theorem ... not achieved (see, e.g., Exercise 1.17). The theory of min- imal surfaces provides an interesting setting in which the primal problem (i.e., inf x∈E {ϕ(x) + ψ(x)}) need not have a solution, while...

Ngày tải lên: 04/02/2014, 11:10

... reported. Keywords: Differential- algebraic equation (DAE), partial differential- algebraic equation (PDAE), nonnegative pencil of matrices, parallel method 1. Introduction Recently there has been a growing interest ... November 2007; received in revised form 12 December 2007 Abstract. This note deals with two fully parallel methods for solving linear partial differential- algebraic equations (PDAEs) of the ... 205 Algorithm PFS Step 1. Initialize v 0 := v 0h Step 2. For given m ≥ 0 and v m (an approximation of v h (mτ)) find v m+1,k by solving (in parallel) systems of linear equations (I + τd 2 H k )v m+1,k =...

Ngày tải lên: 13/02/2014, 03:20

... developed by Einstein in 1905. He proposed a model in which a particle at a point (x, y) in the plane jumps during a small time interval δt to a nearby point from the set (x ± δx, y ± δx). Einstein showed ... fourth-order equation. r Linear equations Another classification is into two groups: linear versus nonlinear equations. An equation is called linear if in (1.1), F is a linear function of the unknown ... example, the equation x 7 u x + e xy u y + sin(x 2 + y 2 )u = x 3 is a linear equation, while u 2 x + u 2 y = 1 is a nonlinear equation. The nonlinear equations are often further classified into subclasses...

Ngày tải lên: 16/02/2014, 15:20

... Ordinary Differential Equations multiple of π ,sincesin(π ) = 0, sin(2π) = 0, etc., and integer multiples of π are the only arguments for which the sine function is 0. The equation λa =π , in ... other kinds of linear, homogeneous equations. Later, we will be using the same principle on partial differential equations. To be able to satisfy an unrestricted initial condition, we need two linearly ... where the differential equation is linear and of second order. However, problems in elas- ticity often involve fourth-order equations. In contrast to initial value problems, even the most innocent...

Ngày tải lên: 17/02/2014, 14:20

Ngày tải lên: 14/03/2014, 10:20

Ngày tải lên: 17/03/2014, 14:29