Mixed Boundary Value Problems© 2008 ppt

Ngày tải lên: 28/03/2014, 17:20

... solving two point boundary value problems. In the shooting method (§17.1) we choose values for all of the dependent variables at one boundary. These values must be consistent with any boundary conditions ... (outside North America). required boundary value desired boundary value 1 3 2 y x Figure 17.0.1. Shooting method(schematic). Trial integrations that satisfy theboundary con...

Ngày tải lên: 24/12/2013, 12:16

... coupledfirst-orderequationsthatsatisfy n 1 boundaryconditions at x 1 and n 2 = N −n 1 boundary conditions at x 2 . Wefirstdefineameshorgridbyasetofk=1,2, , M points at which we supply values for the independent ... unknowns. The remaining N equations come from the boundary conditions. At the first boundary we have 0=E 1 ≡B(x 1 ,y 1 )(17.3.4) while at the second boundary 0=E M+1 ≡ C(x M ,...

Ngày tải lên: 24/12/2013, 12:16

... the eigenvalues up to moderate values of n − m. Since the boundary condition at x =0does not involve y 1 if n − m is even, we have to use the indexv feature of solvde. Recall that the value of ... points at x = ±1 and is to be solved subject to the boundary conditions that the solution be regular at x = ±1. Only for certain valuesofλ, the eigenvalues, willthisbepossible. If we consider...

Ngày tải lên: 21/01/2014, 18:20

... problems, you have to choose values for the independent variable at the mesh points. This is called allocating the grid or mesh. The usual procedure is to pick a plausible set of values and, if it works,

Ngày tải lên: 21/01/2014, 18:20

... derivations of the heat and wave equations. The principal objective of the book is solving boundary value problems involving partial differential equations. Separation of variables receives the greatest ... (x 2 ) +···+f (x r )  · 2a r . The occurrences of 2a cancel, and the computed value is just the average of the functional values. We use a caret over the usual coefficient name to de...

Ngày tải lên: 17/02/2014, 14:20

... form of the boundary conditions (17.0.2), can write a function that generates a complete set of N starting values y, satisfying the boundary conditions at x 1 , from an arbitrary vector value of ... N starting values y i to be specified, but subject to n 1 conditions. Therefore there are n 2 = N − n 1 freely specifiable starting values. Let us imagine that these freely specifiable values a...

Ngày tải lên: 24/12/2013, 12:16

... number of boundary conditions imposed at x 1 is n 1 ,andthe number imposed at x 2 is n 2 , then there are n 2 freely specifiable starting values at x 1 and n 1 freely specifiable starting values at ... f[]) Routine for use with newt to solve a two point boundary value problem for nvar coupled ODEs by shooting from x1 and x2 to a fitting point xf . Initial values for the nvar ODEs at x1 (x2...

Ngày tải lên: 24/12/2013, 12:16

... Academic Press), pp. 129ff. 17.6 Handling Internal Boundary Conditions or Singular Points Singularities can occur in the interiors of two point boundary value problems. Typically, there is a point x s at ... 784 Chapter 17. Two Point Boundary Value Problems Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN ... meaningful value. This constraint on the so...

Ngày tải lên: 21/01/2014, 18:20