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Здраствуйте. Помогите пожалуйста разобраться. В общем есть пример и мне нужно его разобрать, т.е. например: "Выбираем базисные функции и определяем аппроксимирующую функцию" мне нужно понять для чего выбираем эти функции и т.д. Т.е. подробно расписать решение задания. Решение задания написано на Maple(в приложение). Условие: Методом Ритца найти экстремаль функционала ... где область интегрирования и граничная функция имеют вид: ...
Приложение: > restart; Выбираем базисные функции и определяем аппроксимирующую функцию: > phi0:=(x,y)->x/10+y^2/50; > phi:=(x,y,i,j)->sin(i*Pi*(x-x1)/(x2-x1))*sin(j*Pi*(y-y1)/(y2-y1)); > u:=proc(x,y,M,N)option operator,arrow; local n,m; phi0(x,y)+sum(sum(a[m,n]*phi(x,y,m,n),`m`=1..M),`n`=1..N); end proc;
Разработаем процедуру для автоматического составления и решения уравнений метода Ритца для нашего функционала: > Ritz1:=proc(F,M,N,a)local Fu,eqns,var,eq,i,j,res; Fu:=simplify(int(int(F,x=0..1),y=0..2)); eqns:={}:var:={}: for i from 1 to M do for j from 1 to N do var:=var union {a[i,j]}; eq[i,j]:=diff(Fu,a[i,j])=0; eqns:=eqns union {eq[i,j]}; od:od: res:=solve(eqns,var); assign(res); end proc:
Задаем шаг сечений и строим по три секущих плоскости по х и по у: > hx:=(x2-x1)/4; xs1:=x1+hx; xs2:=x1+2*hx ;xs3:=x1+3*hx; hy:=(y2-y1)/4; ys1:=y1+hy; ys2:=y1+2*hy; ys3:=y1+3*hy;
Задаем количество базисных функций для аппроксимации решения. Решаем задачу в первом приближении, строим трехмерный график функции u(x,y) – решения задачи: > M:=1;N:=1; a:=array(1..M,1..N): F2:=subs(z(x,y)=u(x,y,M,N),F):Ritz1(F2,M,N,a): z1:=u(x,y,M,N);z1short:=evalf[5](z1); p3d_1:=plot3d([0,z1],x=0..1,y=0..2,style=wireframe,color=[GREY,GREEN],view=-0.3..0.2,orientation=[130,70],title=cat(`approximation M = N = `,convert(M,string)),axes=BOXED): plots[display](p3d_1);
Второе приближение: > M:=2;N:=2; a:=array(1..M,1..N): F2:=subs(z(x,y)=u(x,y,M,N),F):Ritz1(F2,M,N,a): z1:=u(x,y,M,N);z1short:=evalf[5](z1); p3d_2:=plot3d([0,z1],x=0..1,y=0..2,style=wireframe,color=[GREY,BLUE],view=-0.3..0.2,orientation=[130,70],title=cat(`approximation M = N = `,convert(M,string)),axes=BOXED): plots[display](p3d_2);
Третье приближение: > M:=3;N:=3; a:=array(1..M,1..N): F2:=subs(z(x,y)=u(x,y,M,N),F):Ritz1(F2,M,N,a): z1:=u(x,y,M,N);z1short:=evalf[5](z1); p3d_3:=plot3d([0,z1],x=0..1,y=0..2,style=wireframe,color=[GREY,RED],view=-0.3..0.2,orientation=[130,70],title=cat(`approximation M = N = `,convert(M,string)),axes=BOXED): plots[display](p3d_3);
Здравствуйте, Azarov88. вот две ссылки где расписан метод Ридца http://cultinfo.ru/fulltext/1/001/008/097/114.htm http://www.intuit.ru/department/calculate/nmdiffeq/7/2.html там все доскональна расписано и приведены примеры, нужно только переложить на свою задачу, Maple не знаю поэтому пояснения по коду могут быть не верными не буду их писать, да и лучше бы вы дописали полное условие задачи, что за функция и наверняка в условии базис предлагается.
Вы явно торопитесь набрать баллы. То что Вы написали, ответом по существу не является. Вам следовало или узнать у автора вопроса, что ему непонятно: или язык, используемый в Maple, или метод Ритца, а также попросить его привести полное условие задания.
Если не трудно, уточните, пожалуйста, что является для Вас непонятным: метод Ритца или решение, записанное на языке, ипользуемом в Maple? И каково полное условие задания?
да тут к сожалению немного не разобрался в сущности ответа на вопрос, мини форумом не пользовался моя вина - согласен. уточнять нужно здесь, буду иметь ввиду.
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