計算方法課程設(shè)計報告 實驗四

計算方法課程設(shè)計報告學號姓名：信息電子技術(shù)學院計算機科學與技術(shù)專業(yè)2009

設(shè)計題目解常微分方程具體要求用改進歐拉及四階龍格庫塔法比較。分析結(jié)果技術(shù)手段實現(xiàn)過程#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改進歐拉：n=");scanf("%d",&n);printf("請輸入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龍格庫塔n=");scanf("%d",&n);printf("請輸入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");設(shè)計結(jié)論結(jié)果;改進歐拉：n=10請輸入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龍格庫塔n=10請輸入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=