数值分析原理课程实验——四阶龙格-库塔（Runge-Kutta）方法

四阶龙格-库塔（Runge-Kutta）方法

方法摘要

待求问题

程序流程

程序代码

/*Matlab函数
function Result = Runge_Kutta(a, b, alpha, N, f, has_x, has_y)
    x0 = a;
    y0 = alpha;
    h = (b-a)/N;
    X = zeros(N, 1);
    Y = zeros(N, 1);
    if(has_x == 0 && has_y == 1)
        for n = 1:N
            K1 = h*subs(f, symvar(f), y0);
            K2 = h*subs(f, symvar(f), y0+1/2*K1);
            K3 = h*subs(f, symvar(f), y0+1/2*K2);
            K4 = h*subs(f, symvar(f), y0+K3);
            X(n) = x0+h;
            Y(n) = y0+(K1+2*K2+2*K3+K4)/6;
            x0 = X(n);
            y0 = Y(n);
        end
    elseif(has_x == 1 && has_y == 0)
        for n = 1:N
            K1 = h*subs(f, symvar(f), x0);
            K2 = h*subs(f, symvar(f), x0+h/2);
            K3 = h*subs(f, symvar(f), x0+h/2);
            K4 = h*subs(f, symvar(f), x0+h);
            X(n) = x0+h;
            Y(n) = y0+(K1+2*K2+2*K3+K4)/6;
            x0 = X(n);
            y0 = Y(n);
        end
    elseif(has_x == 1 && has_y == 1)
        for n = 1:N
            K1 = h*subs(f, symvar(f), [x0, y0]);
            K2 = h*subs(f, symvar(f), [x0+h/2, y0+1/2*K1]);
            K3 = h*subs(f, symvar(f), [x0+h/2, y0+1/2*K2]);
            K4 = h*subs(f, symvar(f), [x0+h, y0+K3]);
            X(n) = x0+h;
            Y(n) = y0+(K1+2*K2+2*K3+K4)/6;
            x0 = X(n);
            y0 = Y(n);
        end
    else
        Result = 'No independent variables!';
        return;
    end
    Result = [X,Y];
end*/
/*C语言程序
#include 
#include 
#include 

int n;
double a, b, fa;

double f(double x, double y) { return -y * y; }
double f_(double x) { return 1.0 / (x + 1.0); }

int main() {
    scanf("%lf%lf%lf%d", &a, &b, &fa, &n);
    double x = a, y = fa, h = (b - a) / n;
    for (int i = 1; i <= n; i++) {
        double k1 = h * f(x, y);
        double k2 = h * f(x + h / 2, y + k1 / 2);
        double k3 = h * f(x + h / 2, y + k2 / 2);
        double k4 = h * f(x + h, y + k3);
        x += h;
        y += 1.0 / 6.0 * (k1 + 2 * k2 + 2 * k3 + k4);
        printf("%.2lf\t%lf\t%.2lf\n", x, y, fabs(f_(x) - y));
    }
    return 0;
}*/

运行结果

牛顿（Newton）迭代法，原文链接：

https://blog.csdn.net/KissMoon_/article/details/116277622

高斯（Gauss）列主元消去法，原文链接：

https://blog.csdn.net/KissMoon_/article/details/116278197

拉格朗日（Lagrange）插值，原文链接：

https://blog.csdn.net/KissMoon_/article/details/116278449

Newton/Gauss/Lagrange/Runge-Kutta实验内容+方法指导+Matlab脚本+Matlab函数+Matlab运行报告+C程序+实验报告，一键下载：

https://download.csdn.net/download/KissMoon_/18244419