parametrix4srm.m

样条函数方法

function [A,B] = parametrix4SRM(N,h)
clear all ; clc
N=6; h=0.1;
Ndim=N+3;
A = zeros(Ndim,Ndim);L = zeros(Ndim,Ndim);
%  A(1,1:4)=[1/3,-1/2,0,1/6];
%         A(2,2:5)=[4/3,-1,0,1/6];
%         A(3,3:6)=[7/3,-3/2,0,1/6];
%         A(end,end:-1:end-3)=[1/3,-1/2,0,1/6];
%         A(end-1,end-1:-1:end-4)=[4/3,-1,0,1/6];
%         A(end-2,end-2:-1:end-5)=[7/3,-3/2,0,1/6]; 
%         for I = 4 : Ndim-3
%             A(I,I:I+3)=[8/3,-3/2,0,1/6];
%         end
%         A = sysMat(A);

%  A(1,1:4) = [1/20,7/120,-1/10,-1/120];
%         A(2,2:5) = [1/3,-11/60,-1/5,-1/120];
%         A(3,3:6) = [37/60,-1/8,-1/5,-1/120];
%         A(end,end:-1:end-3) = [1/20,7/120,-1/10,-1/120];
%         A(end-1,end-1:-1:end-4) = [1/3,-11/60,-1/5,-1/120];
%         A(end-2,end-2:-1:end-5) = [37/60,-1/8,-1/5,-1/120];
%         for I = 4 : Ndim-3
%             A(I,I:I+3)=[2/3,-1/8,-1/5,-1/120];
%         end
%         A = sysMat(A);
% A(1,1:4) = [1/252,43/1680,1/84,1/5040];
%         A(2,2:5) = [151/630,177/840,1/420,1/5040];
%         A(3,3:6) = [599/1260,397/1680,1/42,1/5040];
%         A(end,end:-1:end-3) = [1/252,43/1680,1/84,1/5040];
%         A(end-1,end-1:-1:end-4) = [151/630,177/840,1/420,1/5040];
%         A(end-2,end-2:-1:end-5) = [599/1260,397/1680,1/42,1/5040];
%         for I = 4 : Ndim-3
%             A(I,I:I+3)=[151/315,397/1680,1/42,1/5040];
%         end
        A = sysMat( A );
        H(1,1:4) = [-1/72,-1/80,1/40,1/720];
        H(2,1:5) = [-71/720,-2/9,87/360,7/90,1/720];
        H(3,1:6) = [-19/360,-127/360,-1/72,49/144,7/90,1/720];
        H(end,end:-1:end-3) = -[-1/72,-1/80,1/40,1/720];
        H(end-1,end:-1:end-4) = -[-71/720,-2/9,87/360,7/90,1/720];
        H(end-2,end:-1:end-5) = -[-19/360,-127/360,-1/72,49/144,7/90,1/720];
        for I = 4 : Ndim-3
            H(I,I-3:I+3)=[-1/720,-7/90,-49/144,0,49/144,7/90,1/720];
        end
        
        A(1,1:4) = [3,6,-7,-1];
        A(2,1:5) = [-5,0,14,-8,-1];
        A(3,1:6) = [1,-14,3,19,-8,-1];
        A(end,end:-1:end-3) = -[3,6,-7,-1];
        A(end-1,end:-1:end-4) = -[-5,0,14,-8,-1];
        A(end-2,end:-1:end-5) = -[1,-14,3,19,-8,-1];
        for I = 4 : Ndim-3
            A(I,I-3:I+3)=[1,8,19,0,19,-8,-1];
        end
function [Am] = sysMat(A)
dim=size(A,1);
Am = A;
for I = 4 : dim-3
    for J = 1 : I
       Am(I,J) = A(J,I);
    end
end