sf_runge.m

数值实验中基于matlab的龙格算法

function SF_Runge
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Runge ( 龙格 ) 现象
%
% Oct 2, 2007
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
format
n = 10;
px = -5 : (10/n) : 5;           % 插值点
py = 1./(1 + px.^2);            % 插值点上的函数值
plot(px,py,':')                 % 准确函数图像
hold on
plot(px,py,'m+')                % 插值点

[Ln] = SF_Lagrange(px,py);      % 计算 Lagrange 插值多项式
Lx = -5:0.001:5;                % 绘图点
Ly = polyval(Ln,Lx);            % 计算绘图点上的多项式函数值
plot(Lx,Ly,'r')                 % 多项式 图像

return
[S] = SF_YangTiao(px,py);       % 计算三次样条 插值多项式
for k = 0:9
    Sx = k-5 : 0.001 : k-4;
    Sy = polyval(S(k+1,:),Sx);  % 计算绘图点上的多项式函数值
    plot(Sx,Sy,'r')
end


 %xlabel('number of cycle')
 %ylabel('relative residual')
 %legend(['GAR(',num2str(n),')'],['RGAR(',num2str(n),')'],'Location','NorthEast');
 %hold off