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| | [[File:Rico profile.jpg|200px|thumb|right|Josiah Enrico Syefatiawan]] | | [[File:Rico profile.jpg|200px|thumb|right|Josiah Enrico Syefatiawan]] |
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| | Holaaa | | Holaaa |
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| | Perkenalkan nama saya Josiah Enrico S dari jurusan teknik mesin FTUI. Sebagai salah seorang mahasiswa, saya senang belajar dan berbagi banyak hal baru kepada dunia. Melalui wiki ini, saya akan berbagi kepada kalian tentang apa yang saya pelajari. :) | | Perkenalkan nama saya Josiah Enrico S dari jurusan teknik mesin FTUI. Sebagai salah seorang mahasiswa, saya senang belajar dan berbagi banyak hal baru kepada dunia. Melalui wiki ini, saya akan berbagi kepada kalian tentang apa yang saya pelajari. :) |
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| − | = Metode Numerik = | + | = [[Aplikasi CFD - Josiah Enrico S (1906356286)]] = |
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| − | == Aplikasi Modelica - Metode Numerik/18 November 2020 ==
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| − | | |
| − | Berikut ini adalah contoh penerapan aplikasi OpenModelica untuk membuat 4 algoritma metode numerik dalam mencari ''roots of equation'' (akar persamaan) dari:
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| − | | |
| − | <div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
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| − | | |
| − | ''f(x) = exp^(-x)-(x)''
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| − | | |
| − | ''f'(x) = -exp^(-x)-1''
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| − | | |
| − | ''error maksimum = 0.0000001''
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| − | | |
| − | </div>
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| − | | |
| − | ====1) Newton Raphson (Terbuka)====
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| − | | |
| − | model Newton_Raphson_Algorithm
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| − |
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| − | parameter Real g=1; //guess
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| − | parameter Integer N=20; //max iteration
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| − | parameter Real er=0.0000001; //error maximum
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| − | Real a[N];
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| − | Real y[N];//function
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| − | Real ER[N]; //error
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| − | Real sol; //solution
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| − |
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| − | algorithm
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| − |
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| − | a[1]:=g;
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| − | y[1]:=a[1]-(exp(-a[1])-a[1])/(-exp(-a[1])-1);
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| − | ER[1]:=abs(1-a[1]/y[1]);
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| − |
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| − | for i in 2:N loop
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| − | a[i]:=y[i-1];
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| − | y[i]:=a[i]-(exp(-a[i])-a[i])/(-exp(-a[i])-1);
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| − | ER[i]:=abs(1-y[i-1]/y[i]);
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| − |
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| − | if ER[i]<er then
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| − | sol:=y[i];
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| − | break;
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| − | end if;
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| − | end for;
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| − |
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| − | end Newton_Raphson_Algorithm;
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| − | | |
| − | ====2) Secant (Terbuka)====
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| − |
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| − | model Secant_Algorithm
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| − |
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| − | parameter Real a=0; //guess
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| − | parameter Real b=1; //guess
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| − | parameter Integer N=10; //max iteration
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| − | parameter Real er=0.0000001; //error maximum
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| − | Real A[N];
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| − | Real B[N];
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| − | Real y[N];
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| − | Real ER[N];
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| − | Real sol; //solution
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| − |
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| − | algorithm
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| − |
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| − | A[1]:=a;
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| − | B[1]:=b;
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| − | y[1]:=B[1]-(exp(-B[1])-B[1])*(A[1]-B[1])/((exp(-A[1])-A[1])-(exp(-B[1])-B[1]));
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| − | ER[1]:=abs(1-B[1]/y[1]);
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| − |
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| − | for i in 2:N loop
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| − | A[i]:=B[i-1];
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| − | B[i]:=y[i-1];
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| − | y[i]:=B[i]-(exp(-B[i])-B[i])*(A[i]-B[i])/((exp(-A[i])-A[i])-(exp(-B[i])-B[i]));
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| − | ER[i]:=abs(1-y[i-1]/y[i]);
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| − |
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| − | if ER[i]<er then
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| − | sol:=y[i];
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| − | break;
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| − |
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| − | end if;
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| − | end for;
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| − |
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| − | end Secant_Algorithm;
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| − | | |
| − | ====3) Bisection (Tertutup)====
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| − | | |
| − | model Bisection_Algorithm
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| − |
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| − | parameter Real a=0; //guess bawah
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| − | parameter Real b=1; //guess atas
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| − | parameter Integer N=50; //max iteration
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| − | parameter Real er=0.0000001; //error maximum
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| − | Real fa=(exp(-a)-a);
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| − | Real fb=(exp(-b)-b);
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| − | Real A[N];
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| − | Real B[N];
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| − | Real fy[N];
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| − | Real y[N];
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| − | Real ER[N];
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| − | Real sol; //solution
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| − |
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| − | algorithm
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| − |
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| − | if fa*fb<0 then
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| − |
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| − | A[1]:=a;
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| − | B[1]:=b;
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| − | y[1]:=(A[1]+B[1])/2;
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| − | fy[1]:=exp(-y[1])-y[1];
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| − | ER[1]:=1;
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| − |
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| − | for i in 2:N loop
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| − | if fy[i-1]>0 then
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| − | A[i]:=y[i-1];
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| − | B[i]:=B[i-1];
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| − | else
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| − | A[i]:=A[i-1];
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| − | B[i]:=y[i-1];
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| − | end if;
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| − |
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| − | y[i]:=(A[i]+ B[i])/2;
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| − | fy[i]:=exp(-y[i])-y[i];
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| − | ER[i]:=abs(1-y[i-1]/y[i]);
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| − |
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| − | if ER[i]<er then
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| − | sol:=y[i];
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| − | break;
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| − | end if;
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| − |
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| − | end for;
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| − | end if;
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| − |
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| − | end Bisection_Algorithm;
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| − | | |
| − | ====3) Regula Falsi (Tertutup)====
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| − | | |
| − | model Regula_Falsi_Algorithm
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| − |
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| − | parameter Real a=0; //guess bawah
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| − | parameter Real b=1; //guess atas
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| − | parameter Integer N=20; //max iteration
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| − | parameter Real er=0.0000001; //error maximum
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| − | Real A[N];
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| − | Real B[N];
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| − | Real fa[N];
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| − | Real fb[N];
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| − | Real fy[N];
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| − | Real y[N];
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| − | Real ER[N];
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| − | Real sol; //solution
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| − |
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| − | algorithm
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| − |
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| − | A[1]:=a;
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| − | B[1]:=b;
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| − | fa[1]:=exp(-A[1])-A[1];
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| − | fb[1]:=exp(-B[1])-B[1];
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| − |
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| − | if fa[1]*fb[1]<0 then
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| − |
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| − | y[1]:=(A[1]*fb[1]-B[1]*fa[1])/(fb[1]-fa[1]);
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| − | fy[1]:=exp(-y[1])-y[1];
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| − | ER[1]:=1;
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| − |
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| − | for i in 2:N loop
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| − | if fy[i-1]>0 then
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| − | A[i]:=y[i-1];
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| − | B[i]:=B[i-1];
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| − | else
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| − | A[i]:=A[i-1];
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| − | B[i]:=y[i-1];
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| − | end if;
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| − |
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| − | fa[i]:=exp(-A[i])-A[i];
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| − | fb[i]:=exp(-B[i])-B[i];
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| − | y[i]:=(A[i]*fb[i]-B[i]*fa[i])/(fb[i]-fa[i]);
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| − | fy[i]:=exp(-y[i])-y[i];
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| − | ER[i]:=abs(1-y[i-1]/y[i]);
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| − |
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| − | if ER[i]<er then
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| − | sol:=y[i];
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| − | break;
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| − | end if;
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| − | end for;
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| − | end if;
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| − |
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| − | end Regula_Falsi_Algorithm;
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| − | | |
| − | Berikut link Youtube yang berisi penjelasan tentang algoritma dan penulisan kode OpenModelica keempat metode diatas:
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| − | *Tugas 1 Metode Numerik (Youtube): https://www.youtube.com/watch?v=66myoVJuyE0
| + | = [[Metode Numerik - Josiah Enrico S (1906356286)]] = |
| | | | |
| | + | = [[Mekanika Fluida - Josiah Enrico S (1906356286)]] = |
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| | == Gate Valve - Aplikasi CFD/12 November 2020 == | | == Gate Valve - Aplikasi CFD/12 November 2020 == |
