Координати точки (xk+1,
) визначають як точку перетину дотичної у=уk+f(xk,yk)(x-xk) до графіка інтегральної кривої задачі (1.1)-(1.2) в точці (xk,yk) з прямою х=хk [2].2. Розробка алгоритму розв’язання задачі
Стандартний спосіб розв’язання задачі Коші чисельними однокроковими методами – це зведення диференціальних рівнянь n-го порядку до систем з n рівнянь 1-го порядку і подальшого розв’язання цієї системи стандартними однокроковими методами:
Для рівняння
введемо заміну
тоді для даного рівняння можна записати еквівалентну систему із двох рівнянь: ![](data:image/png;base64,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)
Запишемо для кожного з цих рівнянь ітераційне рівняння:
для модифікованого методу :Ейлера:
![](data:image/png;base64,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)
для виправленого методу Ейлера:
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAO8AAACVCAYAAACwya0eAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAu0SURBVHja7Z0xkts2G4Z5gFwgM2G6HMBL/2VcZRTGk9qTNWereFJl1KT2KO7c+ALp0sVFTpCcwDdIkRv4DvktaSlREAACBD4AhJ7imbF3VyQ+Ei/wASLfr3nz5k0DAOuDiwCAeAEA8QIA4gVAvKBlt3v4vGuaf7vh1+99Pzt03e5ht/tcd7ymaf7bs+S4gHjBUbhLRHb4bDfspj97+/anz779svttFPTPm/YXBAyI1xNVSEYRbvsnbdN89BXYr0P3vfqZ3X3/rN/unkzb0H/R/N10L3/nngDiLUS8upRZx8uu+R3xglW8p1H+sNZqP/bb4fkxJdz/+zwblCIs6bb6ivd/w/aHU5tmxKZLmW1xkjaD08x7WGd90f/909u3n7nODqEcZpfHDRotBjFIttVXvOPAsU+H5wYRXcpsPHbbv9/HR2eFWfFOZ7XSR/zYbV0yiKhp8/H/7T828bqnzO270rIeKHzN69IBS0GqrUvXvHNrYNeUeZ9VkC6Dl3gPnevLb38b+nbXNN2/IanoeWa0H2dp2hyzrcnE++n3/f3ume2Y+7S63fz8i89n4MbFq3bYGDudriIIPW7sXVkp8W43mxe2Yx7XzOoAFndggsrEq64fzxsxnzrP46bQtMN2m83r4w7vdcca+v7H8e8lxBuzrSHivXwaqv3YD/2Pp3ZoNq32x9x0m9emDajxoQxT5nGOEzHDgu951VRYt6kiLd6YbV0j6sMcgHi9Nom6zfbVMQ3sXu070uV3r+d07363/SqXeE1tXa1ox5mehzYgpnhLnHlrEy9AsHiPu8P7WfX+iW4mmIr3tJOsrEVTMddWgJsSLwAgXgBAvACIFwAQLwAgXgBAvACIFwAQLwAg3uLZP6N819z9tX9kNJXv8/ScIW2fvnttMxyIca7a7jXiXTnH93WPbzml9n0OdR3ZC3c0CTiIWPPI6zQ+7vfjvRJye+HiRsD5xX3NKJza9/l4vrsPvuJyyRCYcecE7H/dEW8h4p3OXKHiDfF9PszIni9ouLRTFx+EXXcn8WrtVx5PpL6rW+oNyhWDq+vGXdN+UFOnHL7PvrPAtcPHtUuILr5U/trnc6jLkfD03dancs++k5Tr/sl40Om65XBx2vb9eLGXzhShmyMuxnS5YnARr2ktmMP3eckm2dw1s611pb3AdYNULNcUU59aunm1dHPSKW1WT6A3RCt39k0Vg+/Acpy9zOJN6fs8Xh+f+OfEa4pPnR2lBv3DPX4cIEZX0Zjvj8cQ3pLr7iVedY00vShrWVukjsFl5vUTr6zvs60TnTIBNasJEK/roBRr9nXNTEL6VHHi1aUFElv/kn7OqWKInTan9H1OnTZL+mtfDSDt3Yen7dM/Yp4jVv8RS5t1Bx6G4buT0CYzl9o5pDp8jIsjGUPMDauUvs9LNk5cMgJdfNL+2rr7H/P4pj5V1IaV1jN49AtWntox1exx9XKWEq90DKEDkfpVSmrf54u/8+jgVwOC4bNqfK7+2tPBtX/a/GlN52fui85kMOT4tj7lemzddY/hwS2SBs95OUuJVzqGGKO4bnZKvZkn9SBFSHxjar15eHhh/TuLZ7VtoyrG8UPabrruIR7c8W6ch5fz+PVNSeI1xSBxjlxF3GKvuWLHZ1vKuKTEc8XZQo8f2vZp22Kk+Mk6fukzbyrxSs9+JZxzybkOou9evluS8ZxSW4sQQo4f0vZVvJjg4+V8/vt8fs5LYgDZJcvpKbPIfULy+NJtTyJeAEgLFwEA8QIA4gUAxAuAeAEA8QIA4gVAvACAeAEA8QIA4gVAvBCLNZc9AcR7s6y57Akg3uq4hbIngHhvWrxrLnsCBYrXpWzEGsqe5Iyj9rIn53R/3WVxqpx5bWUjcpU9WeLdnCuOmyh7UmBZHMQ77VyashFrK3uSKo5bK3tiEv4ay+JUJ15T2Yi1lT3JEUctZU9MJU9sa+g1lsWpcsNKVzYidskQyZInKeOInTaXXvbEFEPOsjiIVzMim5zhY5UMkbZ/TRVHzA2r4sueVFAWp2rxHjvHtW/xXMmQEkqepIgjtKOtteyJ8diJy+LEKBVS98zrWd+0xJInUnHEaFfNZU9S9ZGQUiFVr3mXbPGXVvIkZhzRxVN52RPJPiJRDXD14nUpGxHS6VPNvNJxrHn2y/1iQg1lcYpf8y6hhpInLnEAfaQ68QIA4gUAxAuAeAEA8QIA4gVAvACAeAEA8QIA4l0VsZ8/nr4XbXs5H0/nfPfb99pz4QoW7hIfZ5Nwx1cQDyLWPGooaVIAjvfd82UVLlpinL2dIxm4uczgzLilCdjNIIELVrt4HY6j85GGfLiaJChp07VDwmhB+s12+/XUT/jiHczC37opKTZf8fr4OGs7wUXc164cOmOAy/dr958Znh/TeLsVrcRAN+fBnbP/5J59zx/Q+PEO2/65asdyDsTdXzgmSwzpSorNV7yhbZmbeW1r3YP4H9fHrjazUgLWeXAnS2UNXtXSex5zWdfsB+eM0dZUtCpXbIsGnEhtmROvyYpWnflymqebPLhz9x/p88wtZfQd7aog1VwHX4czfgmxLV3z2tpi81kOEW8pg7PJgzt3/ylKvLqUIFUHl/ZxzhmbtHil0uZxlhv6dhcjVQzxYdZ5cKdsQ6x02eX83mmzyY83ZQeX8isqIbZSxWtyslTbGWvWWXqPY5rO+bbB1H+kzu+9YaX14727++uiuvpm8/q8yaP+X7+ZYvPpTW5IFzE2SW9nXx9n511SQ8dXvypS17rnzbNLL6mp0Xr/tPlTl+bF9GHWGdalaIPNq9qlDb79fPpVka1dibb69T69a3UKTOHtnHojZqmP9Jhabx4eXuh+H8uH2bZRlaoNS6+D1/kND8zo2iXfMRSrz4vvVBP7OEvGtXbz75CNKbWsiYQP85wHd4o2+FyHJX7luvTc1q6snXzNHr21idc26s+Kvnv5zpR9hN5jFw9u6TaEXgentL3EFxNsPr1r9ujF2/k8u5yeAtPcN+l7vIY2SJ3/pjobQE1wEQAQLwAgXgBAvACIFwAQLwAgXgDECwCIFwAQLwAg3pWSyjcJEC8ICDe3ARwgXpiQ2nwdEC8gXihNvLPu9A/dq7VWTigxtpSVE/bYXP9V1wdKn6xw5jW602sM0HJWTlhi/1pabMkrJxhc/w/XpW3fj8djpl9x2mxyp6+hckLu2HJWTjgdT9m91s7IzL7rFK/Jnb6GygklxZa6csLFADL5/XRAQxAVbFjp3OlTdHDpqgk5Y0shXrd17+W1jV04K6QqAkQQr85uMmXZE0kHyZyx5RSvyfV/ahg+zr6qjWpp9xAs4t0ztTO9dPCPW10gh/1rqthCO3isygmnjMOQoajXwLT2Dr2HrpURIHTmjVRGsbSqCSljq4XY93BpVQJwXPPGTBFLqpogHVutnTLGPYxZLAwU8bq408fu4MmLjSWMrWbx1lL5oso1b0xqrZowF1tN1HwPES8AIF4AQLwAiBcAEC8AIF4AxAsAiBcAEC8AIN7cLPVfHrpup3vM8OptKGxrEC/ICddXZIfPdcNO/bn67PD43DYCRrzggaSF69Sq5+JYyit1p1f2eFsH8UIZ4jWlzDpUbyq4IfFeevfuXRqG58dUL42dq69gSmmrlP+yKWW2XQ/S5hufeQ/rp8dXuXxG/hCWGsrlaGuoeF39l00ps/HYbf+e1+9uXLzTWa30kTxXW1P4L/ulzHXa78CCNe8aDNRLaauI/7JHyhzb1gdWLN7RoG3o212oy5+0D3PMtvq0V1y8n37X3++ezZ1btWh1/RxUKF61I8bYwZTyM5Jo65L2Soh3u9m8mDuevkwJlqo3KV51/XjeYLn2IprzKp56GkmIV6qtUuL18V/eH2/TbV7bNp+0Hsy6qn94SN3emtcntdRtlkiLV6qtudsLICre82x2aQOq1ngd07j73farnGLwaWsK32iA4sRb4szr21ZmXqhevHNexVNB5Pbw9WlrCe0FEBUvACBeAEC8AIgXAFbA/wGIcM0empjcwQAAAABJRU5ErkJggg==)
Таким чином знаходиться масив точок функції ymn з різними кроками тобто n1=(b-a)/0,1=10+1 раз з кроком 0,1 і n2=(b-a)/0,05 раз з кроком 0,05. Це необхідно для оперативного визначення похибки за методом Рунге (екстраполяції Рідчардсона) [3].
Загальний вигляд похибки для цих двох методів
, де с визначається саме за методом Рунге
, звідки с на кожному кроці обчислень знаходиться за формулою:
.Знаючи с можна знайти локальну похибку і просумувавши її по всьому діапазону інтегрування визначити загальну похибку обчислень.
Мовою програмування було обрано Turbo C++. Вона виявилась найзручнішою із тих мов, в яких мені доводилось працювати.
Програма складається з трьох допоміжних функцій float f(x,y,z), void eylermod() i eylerisp(). eylermоd() реалізовує модифікований метод Ейлера, eylerisp() – виправлений метод, а функція f(x,y,z) повертає значення другої похідної рівняння.
Лістинг програми приведено в додатку.
3. Результати обчислень і оцінка похибки
Результатом розв’язання задачі Коші являється функція. В даному випадку отримати цю функцію в аналітичному вигляді обчислювальні однокрокові методи не дозволяють. Вони представляють функцію в табличному вигляді, тобто набір точок значень х і відповідних їм значень функції у(х). Тому для більшої наглядності було вирішено по цим точкам намалювати графіки функцій у(х) для кожного з методів окремо (дивись рисунок 4). На тому ж малюнку виведені значення похибок для кожного методу окремо. На рисунку 5 виведено значення функції у(х) в дискретному вигляді з кроком h1=0.1.
![](data:image/png;base64,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)
Рисунок 4.
![](data:image/png;base64,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)
Рисунок 5.
Висновки
В даній курсовій роботі я ознайомився з однокроковими методами розв’язання звичайних диференціальних рівнянь. Завдяки їй я остаточно розібрався застосовуванням цих методів до розв’язання диференціальних рівнянь вищих порядків на прикладі рівняння другого порядку.
Література
1. Мудров А.Е. Численные методы для ПЭВМ на языках Бейсик, Фортран и Паскаль. – Томск: МП «Раско», 1991. – 272 с.
2. Бортків А.Б., Гринчишин Я.Т. Turbo Pascal: Алгоритми і програми: чисельні методи в фізиці і математиці. Навчальний посібник. – К.: Вища школа, 1992. – 247 с.
3. Квєтний Р.Н. Методи комп’ютерних обчислень. Навчальний посібник. – Вінниця: ВДТУ, 2001 – 148 с.
Додаток
Лістинг програми
#include<stdio.h>
#include<conio.h>
#include<math.h>
#include<graphics.h>
float f(float x,float y,float z)
{return 0.7*z+x*y+0.7*x;}
float h1=0.1;
float h2=0.05;
float a=0;
float b=1;
float x2[21],ye2[21],ym1[11],zm2[21],ym2[21],ye1[11];
float ze1[11],zm1[11],ze2[21],x1[11],yi1[11],yi2[21];
float zi1[11],zi2[21];
int n1=(b-a)/h1;
int n2=(b-a)/h2;
void eylermod()
{// printf("[0] %5.2f %5.2f %5.2f",x2[0],y2[0],z2[0]);
// moveto((x2[0])*100,480-((ym2[0])*100));
for(int i=1;i<=n2+1;i++)
{x2[i]=x2[i-1]+h2;
ze2[i]=ze2[i-1]+h2*f(x2[i-1],ye2[i-1],ze2[i-1]);
ye2[i]=ye2[i-1]+h2*ze2[i-1];
zm2[i]=zm2[i-1]+(h2/2)*(f(x2[i-1],ye2[i-1],zm2[i-1])+f(x2[i],ye2[i],ze2[i]));
ym2[i]=ym2[i-1]+(h2/2)*(ze2[i]+zm2[i-1]);
// printf("\n[%d] %5.2f %5.2f %5.2f",i,x2[i],ye2[i],ym2[i]);
// setcolor(YELLOW);
// lineto((x2[i])*100,480-((ym2[i])*100));}
moveto((x1[0])*250+20,480-((ym1[0])*100)-30);
for(i=1;i<=n1+1;i++)
{x1[i]=x1[i-1]+h1;
ze1[i]=ze1[i-1]+h1*f(x1[i-1],ye1[i-1],ze1[i-1]);
ye1[i]=ye1[i-1]+h1*ze1[i-1];
zm1[i]=zm1[i-1]+(h1/2)*(f(x1[i-1],ye1[i-1],zm1[i-1])+f(x1[i],ye1[i],ze1[i]));
ym1[i]=ym1[i-1]+(h1/2)*(ze1[i]+zm1[i-1]);
// printf("\n[%d] %5.2f %5.2f %5.2f",i,x1[i],ye1[i],ym1[i]);
setcolor(12);
lineto((x1[i])*250+20,480-((ym1[i])*100)-30);}
float c;
float s=0;
for(i=0;i<=n1+1;i++)
{c=(ym2[i*2]-ym1[i])/(h1*h1*h1-h2*h2*h2);
s+=c*h1*h1*h1;}
char *ch;
sprintf(ch,"%f",fabs(s));
setcolor(15);
settextstyle(0,0,1);
outtextxy(5,108,"Похибка:");
settextstyle(2,0,5);
outtextxy(70,102,ch);}
void eylerisp()
{// printf("[0] %5.2f %5.2f %5.2f",x2[0],y2[0],z2[0]);
// moveto((x2[0])*100,480-((ym2[0])*100));
for(int i=1;i<=n2+1;i++)
{x2[i]=x2[i-1]+h2/2;