计算方法课程设计报告 实验四

计算方法课程设计报告学号姓名：信息电子技术学院计算机科学与技术专业2009

设计题目解常微分方程具体要求用改进欧拉及四阶龙格库塔法比较。分析结果技术手段实现过程#include<stdlib.h>#include<stdio.h>#include<math.h>floatf(floatx,floaty){floatf1;f1=x*x-y*y;returnf1; }voidoula(floatx0,floaty0,floath,floatx1,floaty1,floatk1,floatk2){intn,i;printf("\n改进欧拉：n=");scanf("%d",&n);printf("请输入x0,y0,h的值：");scanf("%f,%f,%f",&x0,&y0,&h);for(i=1;i<=n;i++){x1=x0+h;k1=f(x0,y0)*h;k2=f(x1,y0+k1)*h;y1=y0+1.0/2*k1+1.0/2*k2;printf("\n\nx%d=%f",i,x1);printf("\ny%d=%f",i,y1);x0=x1;y0=y1;}}voidlonggekuta(floatx0,floaty0,floath,floatx1,floaty1,floatk1,floatk2,floatk3,floatk4){intn,i;printf("\n龙格库塔n=");scanf("%d",&n);printf("请输入x0,y0,h的值：");scanf("%f,%f,%f",&x0,&y0,&h);for(i=1;i<=n;i++){x1=x0+h;k1=f(x0,y0);k2=f(x0+h/2,y0+k1/2);k3=f(x0+h/2,y0+k2/2);k4=f(x1,y0+k3);y1=y0+1.0/6*(k1+2*k2+2*k3+k4);printf("\n\nx%d=%f",i,x1);printf("\ny%d=%f",i,y1);x0=x1;y0=y1;}}intmain(){floatx0,y0,h,x1,y1,k1,k2,k3,k4;oula(x0,y0,h,x1,y1,k1,k2);printf("\n");longgekuta(x0,y0,h,x1,y1,k1,k2,k3,k4);system("pause");设计结论结果;改进欧拉：n=10请输入x0,y0,h的值：-1,0,0.1x1=-0.900000y1=0.090000x2=-0.800000y2=0.160647x3=-0.700000y3=0.213391x4=-0.600000y4=0.250290x5=-0.500000y5=0.273737x6=-0.400000y6=0.286249x7=-0.300000y7=0.290329x8=-0.200000y8=0.288383x9=-0.100000y9=0.282690x10=0.000000y10=0.275394龙格库塔n=10请输入x0,y0,h的值：-1,0,0.1x1=-0.900000y1=0.678901x2=-0.800000y2=0.781645x3=-0.700000y3=0.742965x4=-0.600000y4=0.665842x5=-0.500000y5=0.580060x6=-0.400000y6=0.494388x7=-0.300000y7=