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Matlab_Code (0, 2016-12-01)
Matlab_Code\.DS_Store (10244, 2017-09-07)
__MACOSX (0, 2018-01-27)
__MACOSX\Matlab_Code (0, 2018-01-27)
__MACOSX\Matlab_Code\._.DS_Store (120, 2017-09-07)
Matlab_Code\Chap10 (0, 2016-12-01)
Matlab_Code\Chap10\ivp_ex2.m (277, 2016-09-18)
__MACOSX\Matlab_Code\Chap10 (0, 2018-01-27)
__MACOSX\Matlab_Code\Chap10\._ivp_ex2.m (239, 2016-09-18)
Matlab_Code\Chap10\prey_prd.m (170, 2016-09-18)
__MACOSX\Matlab_Code\Chap10\._prey_prd.m (239, 2016-09-18)
Matlab_Code\Chap10\prey_prd_drive.m (540, 2016-09-18)
__MACOSX\Matlab_Code\Chap10\._prey_prd_drive.m (239, 2016-09-18)
Matlab_Code\Chap10\yp.m (227, 2016-09-18)
__MACOSX\Matlab_Code\Chap10\._yp.m (239, 2016-09-18)
__MACOSX\Matlab_Code\._Chap10 (239, 2016-12-01)
Matlab_Code\Chap2 (0, 2016-12-01)
Matlab_Code\Chap2\bw_at_b.m (1421, 2016-06-20)
__MACOSX\Matlab_Code\Chap2 (0, 2018-01-27)
__MACOSX\Matlab_Code\Chap2\._bw_at_b.m (239, 2016-06-20)
Matlab_Code\Chap2\compare.m (1350, 2016-06-20)
__MACOSX\Matlab_Code\Chap2\._compare.m (239, 2016-06-20)
Matlab_Code\Chap2\compareb.m (1350, 2016-06-20)
__MACOSX\Matlab_Code\Chap2\._compareb.m (239, 2016-06-20)
Matlab_Code\Chap2\doc (904, 2016-08-09)
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Matlab_Code\Chap2\doc (Zhilin Li's conflicted copy 2015-12-31) (817, 2016-07-16)
__MACOSX\Matlab_Code\Chap2\._doc (Zhilin Li's conflicted copy 2015-12-31) (239, 2016-07-16)
Matlab_Code\Chap2\doc (Zhilin Li's conflicted copy 2016-10-02) (161, 2016-06-20)
__MACOSX\Matlab_Code\Chap2\._doc (Zhilin Li's conflicted copy 2016-10-02) (239, 2016-06-20)
Matlab_Code\Chap2\f.m (44, 2016-06-08)
__MACOSX\Matlab_Code\Chap2\._f.m (239, 2016-06-08)
Matlab_Code\Chap2\ghost_and_bw.m (969, 2016-06-20)
__MACOSX\Matlab_Code\Chap2\._ghost_and_bw.m (239, 2016-06-20)
Matlab_Code\Chap2\ghost_and_bw_org.m (917, 2016-06-20)
__MACOSX\Matlab_Code\Chap2\._ghost_and_bw_org.m (239, 2016-06-20)
Matlab_Code\Chap2\ghost_at_b.m (1364, 2016-06-20)
__MACOSX\Matlab_Code\Chap2\._ghost_at_b.m (239, 2016-06-20)
Matlab_Code\Chap2\main.m (480, 2016-06-08)
__MACOSX\Matlab_Code\Chap2\._main.m (239, 2016-06-08)
... ...

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % % Matlab program for one-dimensional finite element method for % % % % -(k(x)u_x)_x + c(x) u_x + b(x) u(x) = f(x) % % % % with different boundary condition at x =0, and x = l % % % %--------------------------------------------------------------------% fem1d.m: The main drive program. setint.m: Set the nodal points and weights for the Gaussian Quadrature formula in the interval [0,1] of order 1, 2, 3, 4. propset.m: Input the data, form the partition. a, b: a < b, the two end points. inf_ele = 1, or 2, or 3. The basis function of linear, quadratic, or cubic. Could be modified as kind(i) for i-th element. nnode: The number of nodal points. If inf_ele = 1, nnode can be any number >=2. If inf_ele = 2, nnode should be any number, 2k+1, k >=1. If inf_ele = 3, nnode should be a number 3k + 1. The stiffness matrix gk has the dimension nnode by nnode. nelem = (nnode - 1)/inf_ele; The number of elements. x: xcoordinates of all nodal points numbered consecutively from 1 through nnode. nint(i), i=1, ..., nelem = 1, or 2, or 3, or 4. The order of Gaussian quadrature in the i-th element. kind(i), i=1, ..., nelem, = 1, or 2, or 3. The basis function in the i-th element. For uniform triangulation, kind(i) = inf_ele. nodes(j,i), i=1, ..., nelem, j=1, ..., kind(i) + 1, nodal point number of nodes in element, for example, if we use quadratic element, in the second Boundary conditions: kbc(1): BC at x=a, 1: Dirichlet BC, 2: Neumann BC. 3: Mixed BC. kbc(2): BC at x=b, has the same meaning as above. ua: The solution at x=a if Dirichlet BC is chosen. ub: The solution at x=b if Dirichlet BC is chosen. uxa: -k(a) u_x(a) for the Neumann BC at x=a. uxb: k(b) u_x(b) for the Neumann BC at x=b. uxma, uaa for the mixed BC at x = a. It should have the form: k(a) u_x(a) = uxma (u(a) - uaa). uxmb, ubb for the mixed BC at x = b. It should have the form: -k(b) u_x(b) = uxmb (u(b) - ubb). element, we have nodes(1,2)=2, nodes(2,2)=3, nodes(3,i). %------------------------------------------------------------------------ formkf.m Form the discrete linear system by calling elem.m and assemb.m through each element. elem.m Form the local stiffness matrix and load vector. assemb.m Assemble the global stiffness matrix and load vector. shape.m Calculate the values of the basis functions and their derivatives at a point xi. getmat.m Access the material parameters of the differential equation. aplybc.m Adjust the boundary conditions at two end points. If it has a Dirichlet BC at x = a, it will call drchlta.m. If it has a Dirichlet BC at x = b, it will call drchltb.m. drchlta.m drchlta.m %--------------------------------------------------------------------- Note: The oder of the Gaussian integration rule should equal or greater than the order of the basis function. That is nint(i) >= kind(i) Such restriction is due to the choice of the shape function which has uniform expressions in elements but not between two nodal points. Try to use non-uniform grid.

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