Mercurial > repos > public > sbplib
changeset 887:50d5a3843099 feature/timesteppers
Rename package rk4 to rk
| author | Vidar Stiernström <vidar.stiernstrom@it.uu.se> |
|---|---|
| date | Thu, 15 Nov 2018 16:42:58 -0800 |
| parents | 8894e9c49e40 |
| children | 8732d6bd9890 |
| files | +time/+rk/get_rk4_time_step.m +time/+rk/rk4_stability.m +time/+rk/rungekutta_4.m +time/+rk/rungekutta_6.m +time/+rk4/get_rk4_time_step.m +time/+rk4/rk4_stability.m +time/+rk4/rungekutta_4.m +time/+rk4/rungekutta_6.m +time/Rk4SecondOrderNonlin.m +time/Rungekutta4.m +time/Rungekutta4SecondOrder.m +time/Rungekutta4proper.m |
| diffstat | 12 files changed, 124 insertions(+), 124 deletions(-) [+] |
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--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/+time/+rk/get_rk4_time_step.m Thu Nov 15 16:42:58 2018 -0800 @@ -0,0 +1,21 @@ +% Calculate the size of the largest time step given the largest evalue for a operator with pure imaginary e.values. +function k = get_rk4_time_step(lambda,l_type) + default_arg('l_type','complex') + + rad = abs(lambda); + if strcmp(l_type,'real') + % Real eigenvalue + % kl > -2.7852 + k = 2.7852/rad; + + elseif strcmp(l_type,'imag') + % Imaginary eigenvalue + % |kl| < 2.8284 + k = 2.8284/rad; + elseif strcmp(l_type,'complex') + % |kl| < 2.5 + k = 2.5/rad; + else + error('l_type must be one of ''real'',''imag'' or ''complex''.') + end +end \ No newline at end of file
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/+time/+rk/rk4_stability.m Thu Nov 15 16:42:58 2018 -0800 @@ -0,0 +1,58 @@ +function rk_stability() + ruku4 = @(z)(abs(1 + z +(1/2)*z.^2 + (1/6)*z.^3 + (1/24)*z.^4)); + circ = @(z)(abs(z)); + + + % contour(X,Y,z) + ax = [-4 2 -3 3]; + % hold on + fcontour(ruku4,[1,1],[-3, 0.6],[-3.2, 3.2]) + hold on + r = 2.6; + fcontour(circ,[r,r],[-3, 0.6],[-3.2, 3.2],'r') + hold off + % contour(X,Y,z,[1,1],'b') + axis(ax) + title('4th order Runge-Kutta stability region') + xlabel('Re') + ylabel('Im') + axis equal + grid on + box on + hold off + % surf(X,Y,z) + + + rk4roots() +end + +function fcontour(f,levels,x_lim,y_lim,opt) + default_arg('opt','b') + x = linspace(x_lim(1),x_lim(2)); + y = linspace(y_lim(1),y_lim(2)); + [X,Y] = meshgrid(x,y); + mu = X+ 1i*Y; + + z = f(mu); + + contour(X,Y,z,levels,opt) + +end + + +function rk4roots() + ruku4 = @(z)(abs(1 + z +(1/2)*z.^2 + (1/6)*z.^3 + (1/24)*z.^4)); + % Roots for real evalues: + F = @(x)(abs(ruku4(x))-1); + real_x = fzero(F,-3); + + % Roots for imaginary evalues: + F = @(x)(abs(ruku4(1i*x))-1); + imag_x1 = fzero(F,-3); + imag_x2 = fzero(F,3); + + + fprintf('Real x = %f\n',real_x) + fprintf('Imag x = %f\n',imag_x1) + fprintf('Imag x = %f\n',imag_x2) +end \ No newline at end of file
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/+time/+rk/rungekutta_4.m Thu Nov 15 16:42:58 2018 -0800 @@ -0,0 +1,10 @@ +% Takes one time step of size k using the rungekutta method +% starting from v_0 and where the function F(v,t) gives the +% time derivatives. +function v = rungekutta_4(v, t , k, F) + k1 = F(v ,t ); + k2 = F(v+0.5*k*k1,t+0.5*k); + k3 = F(v+0.5*k*k2,t+0.5*k); + k4 = F(v+ k*k3,t+ k); + v = v + (1/6)*(k1+2*(k2+k3)+k4)*k; +end \ No newline at end of file
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/+time/+rk/rungekutta_6.m Thu Nov 15 16:42:58 2018 -0800 @@ -0,0 +1,31 @@ +% Takes one time step of size k using the rungekutta method +% starting from v_0 and where the function F(v,t) gives the +% time derivatives. +function v = rungekutta_6(v, t , k, F) + s = 7 + k = zeros(length(v),s) + a = zeros(7,6); + c = [0, 4/7, 5/7, 6/7, (5-sqrt(5))/10, (5+sqrt(5))/10, 1]; + b = [1/12, 0, 0, 0, 5/12, 5/12, 1/12]; + a = [ + 0, 0, 0, 0, 0, 0; + 4/7, 0, 0, 0, 0, 0; + 115/112, -5/16, 0, 0, 0, 0; + 589/630, 5/18, -16/45, 0, 0, 0; + 229/1200 - 29/6000*sqrt(5), 119/240 - 187/1200*sqrt(5), -14/75 + 34/375*sqrt(5), -3/100*sqrt(5), 0, 0; + 71/2400 - 587/12000*sqrt(5), 187/480 - 391/2400*sqrt(5), -38/75 + 26/375*sqrt(5), 27/80 - 3/400*sqrt(5), (1+sqrt(5))/4, 0; + -49/480 + 43/160*sqrt(5), -425/96 + 51/32*sqrt(5), 52/15 - 4/5*sqrt(5), -27/16 + 3/16*sqrt(5), 5/4 - 3/4*sqrt(5), 5/2 - 1/2*sqrt(5); + ] + + for i = 1:s + u = v + for j = 1: i-1 + u = u + h*a(i,j) * k(:,j) + end + k(:,i) = F(t+c(i)*k,u) + end + + for i = 1:s + v = v + k*b(i)*k(:,i) + end +end
--- a/+time/+rk4/get_rk4_time_step.m Thu Nov 15 16:36:21 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,21 +0,0 @@ -% Calculate the size of the largest time step given the largest evalue for a operator with pure imaginary e.values. -function k = get_rk4_time_step(lambda,l_type) - default_arg('l_type','complex') - - rad = abs(lambda); - if strcmp(l_type,'real') - % Real eigenvalue - % kl > -2.7852 - k = 2.7852/rad; - - elseif strcmp(l_type,'imag') - % Imaginary eigenvalue - % |kl| < 2.8284 - k = 2.8284/rad; - elseif strcmp(l_type,'complex') - % |kl| < 2.5 - k = 2.5/rad; - else - error('l_type must be one of ''real'',''imag'' or ''complex''.') - end -end \ No newline at end of file
--- a/+time/+rk4/rk4_stability.m Thu Nov 15 16:36:21 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,58 +0,0 @@ -function rk_stability() - ruku4 = @(z)(abs(1 + z +(1/2)*z.^2 + (1/6)*z.^3 + (1/24)*z.^4)); - circ = @(z)(abs(z)); - - - % contour(X,Y,z) - ax = [-4 2 -3 3]; - % hold on - fcontour(ruku4,[1,1],[-3, 0.6],[-3.2, 3.2]) - hold on - r = 2.6; - fcontour(circ,[r,r],[-3, 0.6],[-3.2, 3.2],'r') - hold off - % contour(X,Y,z,[1,1],'b') - axis(ax) - title('4th order Runge-Kutta stability region') - xlabel('Re') - ylabel('Im') - axis equal - grid on - box on - hold off - % surf(X,Y,z) - - - rk4roots() -end - -function fcontour(f,levels,x_lim,y_lim,opt) - default_arg('opt','b') - x = linspace(x_lim(1),x_lim(2)); - y = linspace(y_lim(1),y_lim(2)); - [X,Y] = meshgrid(x,y); - mu = X+ 1i*Y; - - z = f(mu); - - contour(X,Y,z,levels,opt) - -end - - -function rk4roots() - ruku4 = @(z)(abs(1 + z +(1/2)*z.^2 + (1/6)*z.^3 + (1/24)*z.^4)); - % Roots for real evalues: - F = @(x)(abs(ruku4(x))-1); - real_x = fzero(F,-3); - - % Roots for imaginary evalues: - F = @(x)(abs(ruku4(1i*x))-1); - imag_x1 = fzero(F,-3); - imag_x2 = fzero(F,3); - - - fprintf('Real x = %f\n',real_x) - fprintf('Imag x = %f\n',imag_x1) - fprintf('Imag x = %f\n',imag_x2) -end \ No newline at end of file
--- a/+time/+rk4/rungekutta_4.m Thu Nov 15 16:36:21 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,10 +0,0 @@ -% Takes one time step of size k using the rungekutta method -% starting from v_0 and where the function F(v,t) gives the -% time derivatives. -function v = rungekutta_4(v, t , k, F) - k1 = F(v ,t ); - k2 = F(v+0.5*k*k1,t+0.5*k); - k3 = F(v+0.5*k*k2,t+0.5*k); - k4 = F(v+ k*k3,t+ k); - v = v + (1/6)*(k1+2*(k2+k3)+k4)*k; -end \ No newline at end of file
--- a/+time/+rk4/rungekutta_6.m Thu Nov 15 16:36:21 2018 -0800 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,31 +0,0 @@ -% Takes one time step of size k using the rungekutta method -% starting from v_0 and where the function F(v,t) gives the -% time derivatives. -function v = rungekutta_6(v, t , k, F) - s = 7 - k = zeros(length(v),s) - a = zeros(7,6); - c = [0, 4/7, 5/7, 6/7, (5-sqrt(5))/10, (5+sqrt(5))/10, 1]; - b = [1/12, 0, 0, 0, 5/12, 5/12, 1/12]; - a = [ - 0, 0, 0, 0, 0, 0; - 4/7, 0, 0, 0, 0, 0; - 115/112, -5/16, 0, 0, 0, 0; - 589/630, 5/18, -16/45, 0, 0, 0; - 229/1200 - 29/6000*sqrt(5), 119/240 - 187/1200*sqrt(5), -14/75 + 34/375*sqrt(5), -3/100*sqrt(5), 0, 0; - 71/2400 - 587/12000*sqrt(5), 187/480 - 391/2400*sqrt(5), -38/75 + 26/375*sqrt(5), 27/80 - 3/400*sqrt(5), (1+sqrt(5))/4, 0; - -49/480 + 43/160*sqrt(5), -425/96 + 51/32*sqrt(5), 52/15 - 4/5*sqrt(5), -27/16 + 3/16*sqrt(5), 5/4 - 3/4*sqrt(5), 5/2 - 1/2*sqrt(5); - ] - - for i = 1:s - u = v - for j = 1: i-1 - u = u + h*a(i,j) * k(:,j) - end - k(:,i) = F(t+c(i)*k,u) - end - - for i = 1:s - v = v + k*b(i)*k(:,i) - end -end
--- a/+time/Rk4SecondOrderNonlin.m Thu Nov 15 16:36:21 2018 -0800 +++ b/+time/Rk4SecondOrderNonlin.m Thu Nov 15 16:42:58 2018 -0800 @@ -67,7 +67,7 @@ end function obj = step(obj) - obj.w = time.rk4.rungekutta_4(obj.w, obj.t, obj.k, obj.F); + obj.w = time.rk.rungekutta_4(obj.w, obj.t, obj.k, obj.F); obj.t = obj.t + obj.k; obj.n = obj.n + 1; end
--- a/+time/Rungekutta4.m Thu Nov 15 16:36:21 2018 -0800 +++ b/+time/Rungekutta4.m Thu Nov 15 16:42:58 2018 -0800 @@ -43,7 +43,7 @@ end function obj = step(obj) - obj.v = time.rk4.rungekutta_4(obj.v, obj.t, obj.k, obj.F); + obj.v = time.rk.rungekutta_4(obj.v, obj.t, obj.k, obj.F); obj.t = obj.t + obj.k; obj.n = obj.n + 1; end
--- a/+time/Rungekutta4SecondOrder.m Thu Nov 15 16:36:21 2018 -0800 +++ b/+time/Rungekutta4SecondOrder.m Thu Nov 15 16:42:58 2018 -0800 @@ -105,7 +105,7 @@ end function obj = step(obj) - obj.w = time.rk4.rungekutta_4(obj.w, obj.t, obj.k, obj.F); + obj.w = time.rk.rungekutta_4(obj.w, obj.t, obj.k, obj.F); obj.t = obj.t + obj.k; obj.n = obj.n + 1; end
--- a/+time/Rungekutta4proper.m Thu Nov 15 16:36:21 2018 -0800 +++ b/+time/Rungekutta4proper.m Thu Nov 15 16:42:58 2018 -0800 @@ -31,7 +31,7 @@ end function obj = step(obj) - obj.v = time.rk4.rungekutta_4(obj.v, obj.t, obj.k, obj.F); + obj.v = time.rk.rungekutta_4(obj.v, obj.t, obj.k, obj.F); obj.t = obj.t + obj.k; obj.n = obj.n + 1; end