From f8ce7b28cca8f51ec8935db9c05e2ded6e6e106b Mon Sep 17 00:00:00 2001 From: Igor Date: Mon, 22 Oct 2012 14:44:52 +0200 Subject: [PATCH] del --- .../runge_kutta_4th_steppin_method.m | 35 ------------- ...kutta_4th_steppin_method_quiz_week2_lec4.m | 36 ------------- .../runge_kutta_4th_steppin_method_rhs.m | 4 -- .../homework1.png | Bin 109216 -> 0 bytes .../hw1 hints.pdf | Bin 300173 -> 0 bytes .../runge_kutta_4th_steppin_method.m | 48 ------------------ .../runge_kutta_4th_steppin_method_rhs.m | 5 -- .../03-Newton solver/newton_solver.m | 3 -- .../bc_bvp.m | 21 -------- .../bc_init.m | 2 - .../boundary_value_solver.m | 31 ----------- .../rhs_bvp.m | 21 -------- .../05-BVS. nonlinear/bc_bvp_nonlinear.m | 4 -- .../05-BVS. nonlinear/bc_init.m | 2 - .../boundary_value_solver_nonlinear.m | 20 -------- .../05-BVS. nonlinear/rhs_bvp_nonlinear.m | 6 --- 16 files changed, 238 deletions(-) delete mode 100644 Scientific computing/01-lecture 4. week 2. Implementation of Shooting and Convergence Studies/runge_kutta_4th_steppin_method.m delete mode 100644 Scientific computing/01-lecture 4. week 2. Implementation of Shooting and Convergence Studies/runge_kutta_4th_steppin_method_quiz_week2_lec4.m delete mode 100644 Scientific computing/01-lecture 4. week 2. Implementation of Shooting and Convergence Studies/runge_kutta_4th_steppin_method_rhs.m delete mode 100644 Scientific computing/02-Homework 1. Quantum Harmonic Oscillator/homework1.png delete mode 100644 Scientific computing/02-Homework 1. Quantum Harmonic Oscillator/hw1 hints.pdf delete mode 100644 Scientific computing/02-Homework 1. Quantum Harmonic Oscillator/runge_kutta_4th_steppin_method.m delete mode 100644 Scientific computing/02-Homework 1. Quantum Harmonic Oscillator/runge_kutta_4th_steppin_method_rhs.m delete mode 100644 Scientific computing/03-Newton solver/newton_solver.m delete mode 100644 Scientific computing/04-Taylor. Implementing boundary value solver/bc_bvp.m delete mode 100644 Scientific computing/04-Taylor. Implementing boundary value solver/bc_init.m delete mode 100644 Scientific computing/04-Taylor. Implementing boundary value solver/boundary_value_solver.m delete mode 100644 Scientific computing/04-Taylor. Implementing boundary value solver/rhs_bvp.m delete mode 100644 Scientific computing/05-BVS. nonlinear/bc_bvp_nonlinear.m delete mode 100644 Scientific computing/05-BVS. nonlinear/bc_init.m delete mode 100644 Scientific computing/05-BVS. nonlinear/boundary_value_solver_nonlinear.m delete mode 100644 Scientific computing/05-BVS. nonlinear/rhs_bvp_nonlinear.m diff --git a/Scientific computing/01-lecture 4. week 2. Implementation of Shooting and Convergence Studies/runge_kutta_4th_steppin_method.m b/Scientific computing/01-lecture 4. week 2. Implementation of Shooting and Convergence Studies/runge_kutta_4th_steppin_method.m deleted file mode 100644 index 4d8df8c..0000000 --- a/Scientific computing/01-lecture 4. week 2. Implementation of Shooting and Convergence Studies/runge_kutta_4th_steppin_method.m +++ /dev/null @@ -1,35 +0,0 @@ -clear all; close all; clc; - -tol=10^(-4);%tolerance -xspan=[-1 1];%finding solution between 2 numbers of xspan - -A=1; -ic=[0 A];%initial conditions - -beta=99;%betta - - - -for jj=1:5% for finding more than 1 solution -dbeta=1; - -for j=1:1000 - -[t,y]=ode45('runge_kutta_4th_steppin_method_rhs',xspan,ic,[],beta); - -if abs(y(end,1))0% last component of 1st column in power of jj+1, - %becouse after first solution the function become negative(like sin) - %will be -beta=beta-dbeta; % если больше то спускаемся ниже -else -beta=beta+dbeta;% усли ниже, то промахнулись возврат -dbeta=dbeta/2;%и меняем шаг -end -end -beta -beta=beta-1; -plot(t,y(:,1)),hold on -end \ No newline at end of file diff --git a/Scientific computing/01-lecture 4. week 2. Implementation of Shooting and Convergence Studies/runge_kutta_4th_steppin_method_quiz_week2_lec4.m b/Scientific computing/01-lecture 4. week 2. Implementation of Shooting and Convergence Studies/runge_kutta_4th_steppin_method_quiz_week2_lec4.m deleted file mode 100644 index 3b2b250..0000000 --- a/Scientific computing/01-lecture 4. week 2. Implementation of Shooting and Convergence Studies/runge_kutta_4th_steppin_method_quiz_week2_lec4.m +++ /dev/null @@ -1,36 +0,0 @@ -clear all; close all; clc; - -tol=10^(-6);%tolerance -xspan=[-1 1];%finding solution between 2 numbers of xspan - -A=1; -ic=[0 A];%initial conditions y(0) y'(A) - -beta=91;%betta - - - -% for jj=1:5% for finding more than 1 solution -% dbeta=1; -% -% for j=1:1000 - -[t,y]=ode45('runge_kutta_4th_steppin_method_rhs',xspan,ic,[],beta); - -% if abs(y(end,1))0% last component of 1st column in power of jj+1, -% %becouse after first solution the function become negative(like sin) -% %will be -% beta=beta-dbeta; % если больше то спускаемся ниже -% else -% beta=beta+dbeta;% усли ниже, то промахнулись возврат -% dbeta=dbeta/2;%и меняем шаг -% end -% end -beta -% beta=beta-1; -y(end,1) -% % plot(t,y(:,1)),hold on -% end \ No newline at end of file diff --git a/Scientific computing/01-lecture 4. week 2. Implementation of Shooting and Convergence Studies/runge_kutta_4th_steppin_method_rhs.m b/Scientific computing/01-lecture 4. week 2. Implementation of Shooting and Convergence Studies/runge_kutta_4th_steppin_method_rhs.m deleted file mode 100644 index f827d42..0000000 --- a/Scientific computing/01-lecture 4. week 2. Implementation of Shooting and Convergence Studies/runge_kutta_4th_steppin_method_rhs.m +++ /dev/null @@ -1,4 +0,0 @@ -function rhs=runge_kutta_4th_steppin_method_rhs(x,ic,dummy,beta) -y1=ic(1); -y2=ic(2); -rhs=[y2;(beta-100)*y1]; \ No newline at end of file diff --git a/Scientific computing/02-Homework 1. Quantum Harmonic Oscillator/homework1.png b/Scientific computing/02-Homework 1. 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Quantum Harmonic Oscillator/runge_kutta_4th_steppin_method.m b/Scientific computing/02-Homework 1. Quantum Harmonic Oscillator/runge_kutta_4th_steppin_method.m deleted file mode 100644 index 01bb7ab..0000000 --- a/Scientific computing/02-Homework 1. Quantum Harmonic Oscillator/runge_kutta_4th_steppin_method.m +++ /dev/null @@ -1,48 +0,0 @@ -clear all; close all; clc; -format long -tol=10^(-10);%tolerance -xspan=[-4 4];%finding solution between 2 numbers of xspan - -A=1; -ic=[0 A];%initial conditions y(0) y'(A) - -En=16;% не получается что-то этот вывод... -%Y''+betta*y=0,betta should be positive becouse -%we should have several answers there PSI=0 (from ic:PSI(-4,+4)=0) -%thats why sin and cos in answers not exp() -%therefore -(x^2-En)>0 x(max)=+-4 >> - - - -for jj=1:10% for finding more than 1 solution -dEn=1; -if En<0 - break -end -for j=1:1000 - -[t,y]=ode45('runge_kutta_4th_steppin_method_rhs',xspan,ic,[],En); - -if abs(y(end,1))0% last component of 1st column in power of jj+1, - %becouse after first solution the function become negative(like sin) - %will be -En=En-dEn; % если больше то спускаемся ниже -else -En=En+dEn;% усли ниже, то промахнулись возврат -dEn=dEn/2;%и меняем шаг -end -end - - - -En -En=En-1; -y; -plot(t,y(:,1)),hold on -end \ No newline at end of file diff --git a/Scientific computing/02-Homework 1. Quantum Harmonic Oscillator/runge_kutta_4th_steppin_method_rhs.m b/Scientific computing/02-Homework 1. Quantum Harmonic Oscillator/runge_kutta_4th_steppin_method_rhs.m deleted file mode 100644 index 90beaca..0000000 --- a/Scientific computing/02-Homework 1. Quantum Harmonic Oscillator/runge_kutta_4th_steppin_method_rhs.m +++ /dev/null @@ -1,5 +0,0 @@ -function rhs=runge_kutta_4th_steppin_method_rhs(x,ic,dummy,En) -y1=ic(1); -y2=ic(2); -x; -rhs=[y2;(x^2-En)*y1]; \ No newline at end of file diff --git a/Scientific computing/03-Newton solver/newton_solver.m b/Scientific computing/03-Newton solver/newton_solver.m deleted file mode 100644 index 3f8295b..0000000 --- a/Scientific computing/03-Newton solver/newton_solver.m +++ /dev/null @@ -1,3 +0,0 @@ -%Newton solver f = @(x)x.^3-2*x-5; means f(x)=x^3-2x-5 -f=@(x)exp(x)-sin(x) -z=fzero(f,-3) \ No newline at end of file diff --git a/Scientific computing/04-Taylor. Implementing boundary value solver/bc_bvp.m b/Scientific computing/04-Taylor. Implementing boundary value solver/bc_bvp.m deleted file mode 100644 index 0c39c4a..0000000 --- a/Scientific computing/04-Taylor. Implementing boundary value solver/bc_bvp.m +++ /dev/null @@ -1,21 +0,0 @@ -%example y''+3y'+6y=5 -%BC: x [1,3] -%y(1)=3 -%y(3)+2y'(3)=5 -% 1. need transform to 1st order DE -% y1=y ----->y1'=y' -% y2=y' ----->y2'=y'' -% -% -% Our equations -%y1'=y2 -%y2'=5-3y2-6y1 - -%our BC -%y1-3=0 -%y1+2y2-5=0 - -%BC - -function bc=bc_bvp(yl,yr)%also you can specify middle poins -bc=[yl(1)-3;yr(1)+2*yr(2)-5]; diff --git a/Scientific computing/04-Taylor. Implementing boundary value solver/bc_init.m b/Scientific computing/04-Taylor. Implementing boundary value solver/bc_init.m deleted file mode 100644 index ba9edec..0000000 --- a/Scientific computing/04-Taylor. Implementing boundary value solver/bc_init.m +++ /dev/null @@ -1,2 +0,0 @@ -function in=bc_init(x) -in=[cos((pi/2)*x); -(pi/2)*sin((pi/2)*x)]; \ No newline at end of file diff --git a/Scientific computing/04-Taylor. Implementing boundary value solver/boundary_value_solver.m b/Scientific computing/04-Taylor. Implementing boundary value solver/boundary_value_solver.m deleted file mode 100644 index 23a0fda..0000000 --- a/Scientific computing/04-Taylor. Implementing boundary value solver/boundary_value_solver.m +++ /dev/null @@ -1,31 +0,0 @@ -%example y''+3y'+6y=5 -%BC: x [1,3] -%y(1)=3 -%y(3)+2y'(3)=5 -% 1. need transform to 1st order DE -% y1=y ----->y1'=y' -% y2=y' ----->y2'=y'' -% -% -% Our equations -%y1'=y2 -%y2'=5-3y2-6y1 - -%our BC -%y1-3=0 -%y1+2y2-5=0 - -clear all; close all; clc; - -%default tolerance in matlab is 10^-6 - -init=bvpinit(linspace(1,3,10),[0 0]);%guessing for 10 point solution is -%y1=0 and y2=0 (it is not BC) -%but program will make it not 0.2=dx, -%Matlab not trust you! will pick dx by itself - - -sol=bvp4c(@rhs_bvp,@bc_bvp,init);%rhs,BC, init- is guess for solution -x=linspace(1,3,100); %linear space of x, devide x onto 100 points -BS=deval(sol,x);%vector, deval calculate it for you for given x -plot(x,BS(1,:)) \ No newline at end of file diff --git a/Scientific computing/04-Taylor. Implementing boundary value solver/rhs_bvp.m b/Scientific computing/04-Taylor. Implementing boundary value solver/rhs_bvp.m deleted file mode 100644 index d9d718c..0000000 --- a/Scientific computing/04-Taylor. Implementing boundary value solver/rhs_bvp.m +++ /dev/null @@ -1,21 +0,0 @@ -%example y''+3y'+6y=5 -%BC: x [1,3] -%y(1)=3 -%y(3)+2y'(3)=5 -% 1. need transform to 1st order DE -% y1=y ----->y1'=y' -% y2=y' ----->y2'=y'' -% -% -% Our equations -%y1'=y2 -%y2'=5-3y2-6y1 - -%our BC -%y1-3=0 -%y1+2y2-5=0 - -function rhs=rhs_bvp(x,y) -rhs=[y(2);-3*y(2)-6*y(1)+5];% in the begining y1=0 because guessing -%working with domain x, initialy its 10 points -% \ No newline at end of file diff --git a/Scientific computing/05-BVS. nonlinear/bc_bvp_nonlinear.m b/Scientific computing/05-BVS. nonlinear/bc_bvp_nonlinear.m deleted file mode 100644 index 04545c8..0000000 --- a/Scientific computing/05-BVS. nonlinear/bc_bvp_nonlinear.m +++ /dev/null @@ -1,4 +0,0 @@ -%BC - -function bc=bc_bvp_nonlinear(yl,yr,beta)%also you can specify middle poins -bc=[yl(1); yl(2)-1; yr(1)]; diff --git a/Scientific computing/05-BVS. nonlinear/bc_init.m b/Scientific computing/05-BVS. nonlinear/bc_init.m deleted file mode 100644 index ba9edec..0000000 --- a/Scientific computing/05-BVS. nonlinear/bc_init.m +++ /dev/null @@ -1,2 +0,0 @@ -function in=bc_init(x) -in=[cos((pi/2)*x); -(pi/2)*sin((pi/2)*x)]; \ No newline at end of file diff --git a/Scientific computing/05-BVS. nonlinear/boundary_value_solver_nonlinear.m b/Scientific computing/05-BVS. nonlinear/boundary_value_solver_nonlinear.m deleted file mode 100644 index bdd499f..0000000 --- a/Scientific computing/05-BVS. nonlinear/boundary_value_solver_nonlinear.m +++ /dev/null @@ -1,20 +0,0 @@ - - -clear all; close all; clc; - -%default tolerance in matlab is 10^-6 - -%guessing -beta=99;%guess -init=bvpinit(linspace(-1,1,50),@bc_init, beta)%guessing for 10 point -%between BC solution is -% function bc_init -%but program will make it not 0.2=dx, -%Matlab not trust you! will pick dx by itself - - -sol=bvp4c(@rhs_bvp_nonlinear,@bc_bvp_nonlinear,init);%rhs,BC, -%init- is guess for solution -x=linspace(-1,1,100); %linear space of x, devide x onto 100 points -BS=deval(sol,x);%vector, deval calculate it for you for given x -plot(x,BS(1,:)) \ No newline at end of file diff --git a/Scientific computing/05-BVS. nonlinear/rhs_bvp_nonlinear.m b/Scientific computing/05-BVS. nonlinear/rhs_bvp_nonlinear.m deleted file mode 100644 index 42519d8..0000000 --- a/Scientific computing/05-BVS. nonlinear/rhs_bvp_nonlinear.m +++ /dev/null @@ -1,6 +0,0 @@ -%RHS of DEs - -function rhs=rhs_bvp_nonlinear(x,y,beta) -rhs=[y(2);(beta-100)*y(1)-y(1)^3];% in the begining y1=0 because guessing -%working with domain x, initialy its 10 points -% \ No newline at end of file