From f97cd0a0585869ec82a76077f028af3d3325345b Mon Sep 17 00:00:00 2001 From: nin13001 <32068635+nin13001@users.noreply.github.com> Date: Wed, 6 Dec 2017 00:03:42 -0500 Subject: [PATCH] editing --- README.md | 36 +++++++++++++++++++++++++++++++----- assets/README-23f54e97.png | Bin 53314 -> 0 bytes assets/README-4e4bb548.png | Bin 32001 -> 0 bytes assets/README-66741291.png | Bin 41589 -> 0 bytes assets/README-8b7eb1c9.png | Bin 0 -> 49766 bytes assets/README-be88b588.png | Bin 0 -> 41305 bytes assets/README-bec1ab77.png | Bin 0 -> 43985 bytes assets/README-fcbec9a1.png | Bin 0 -> 51551 bytes prob2plot.m | 2 +- prob2ptB.asv | 12 ++++++++++++ prob2ptB.m | 3 ++- prob3plot.asv | 17 +++++++++++++++++ prob3plot.m | 17 +++++++++++++++++ prob3ptB.m | 3 ++- prob3ptC.m | 20 ++++++++++++++++++++ 15 files changed, 102 insertions(+), 8 deletions(-) delete mode 100644 assets/README-23f54e97.png delete mode 100644 assets/README-4e4bb548.png delete mode 100644 assets/README-66741291.png create mode 100644 assets/README-8b7eb1c9.png create mode 100644 assets/README-be88b588.png create mode 100644 assets/README-bec1ab77.png create mode 100644 assets/README-fcbec9a1.png create mode 100644 prob2ptB.asv create mode 100644 prob3plot.asv create mode 100644 prob3plot.m create mode 100644 prob3ptC.m diff --git a/README.md b/README.md index c997aa6..8e9c04d 100644 --- a/README.md +++ b/README.md @@ -16,9 +16,10 @@ for i=2:length(x) dy=prob2_ode(x,y_n(i-1)); y_n(i)=y_n(i-1)+ dt(2)*dy; end -plot(x,exp(-x),'k-',x,y_n,'o'); +plot(x,exp(-x),x,y_n) +legend('Analytical','Euler','Location','Northeast') ``` -![](assets/README-66741291.png) +![](assets/README-be88b588.png) ## Part C @@ -46,7 +47,7 @@ y(1)=y0; end end ``` -![](assets/README-23f54e97.png) +![](assets/README-8b7eb1c9.png) # Problem 3 ## Part A @@ -64,6 +65,31 @@ for i=2:length(x) dy=prob3_ode(x,y_n(i-1,:)); y_n(i,:)=y_n(i-1,:)+ dt(2)*dy; end -plot(x,cos(3*x),'k-',x,y_n(:,1),'o'); +plot(x,cos(3*x),x,y_n(:,1)); ``` -![](assets/README-4e4bb548.png) +![](assets/README-bec1ab77.png) + +## Part C +``` +function y = prob3ptC(prob3_ode, dt, y0,tlimits) + t = [tlimits(1):dt:tlimits(2)]; + y = zeros(length(t),length(y0)); + y(1,:) = y0; + for i = 2:length(t) + dy = prob3_ode(t(i-1),y(i-1,:)); + y(i,:) = y(i-1,:)+dt*dy; + dyc = (dy + prob3_ode(t(i),y(i,:)))/2; + y(i,:) = y(i-1,:)+dt*dyc; + n = 1; + while (1) + n = n+1; + yold = y(i,:); + dyc = (dy+prob3_ode(t(i),y(i,:)))/2; + y(i,:) = y(i-1,:)+dt*dyc; + ea = abs(y(i,:)- yold)./y(i,:)*100; + if max(ea) < 0.0001 || n>100; break, end + end + end +end +``` +![](assets/README-fcbec9a1.png) diff --git a/assets/README-23f54e97.png b/assets/README-23f54e97.png deleted file mode 100644 index a16cda432a292feaa143df042b19514abc9c7f3c..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 53314 zcmeGEbyQSs7(NPPU?2t}pdg5Z2+ANzw&C@J9LJ}t5q?Y?#a$%mIq#$^QRk%<}SS68y)&gz!NSPcBC5-=D;=*RB73Xnoo14B<1+np4m_ 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zv9=@plkg^luDH*8yuyF{BC26dEW0MGNGh5G7F_s-id#y`6W~Aw;mHQi zd`qt{msfvfXmGRq0bvuV@`1ZJy0w)eBgLDEt<#Mp(E4b?D-MMPGel@#3lZlKEYW3& zwT|}vC$Ww2&>u-zCR)ZK)!h>z)Mnfl?@K=hyKM5y$rp@{9)iLQTmIk{~ z+;`CANgfZrW3vi~LuYpX8>Q+_q>+_=2E#_0XiW^ViS5k1Noa_{#e0s^4{mh_gm&g( z_<}{iHS#tZm#`l@k!`g*d3+_(!N|cQDpwXR86?f1<_~LdZsD*w1}fk{os+<}`U8O!G2UTKVM(7&>#_z~rYpd`e5Yj|{rlJhHw2oH6! zw<4v?0%MBGk(bwZNARMKRnhUSiQ)f2FR%YUp%;_q@0QK?K*KS)tgoTEWBTH={8c7o zWr@UgMCG@T%5TJyk5BfFpz44ie561{G#GZtl_)UG`x>$%uo&sc{!{QZh}8aCyLP(? zw(BpZ!rjkhV>v7T!6v#w0PR=>7g+Ns-nqM|6*!7ubk&vp8Jn6d?f2<&`Kv|E LcN(PW9X|UXE#nxr literal 0 HcmV?d00001 diff --git a/prob2plot.m b/prob2plot.m index be9521c..4cd4ea4 100644 --- a/prob2plot.m +++ b/prob2plot.m @@ -11,7 +11,7 @@ for i = 2:length(t) end a = figure(1); y_heun = Prob2ptC (@(t,y) prob2_ode(t,y), 0.1, 1, [0 3]); -plot(t,exp(-t),'k-',t,y,'Xg',t,y_heun,'Or'); +plot(t,exp(-t),t,y,t,y_heun); legend('Analytical','Euler','Heun','Location','Northeast') xlabel('Time') ylabel('Position') \ No newline at end of file diff --git a/prob2ptB.asv b/prob2ptB.asv new file mode 100644 index 0000000..43a380e --- /dev/null +++ b/prob2ptB.asv @@ -0,0 +1,12 @@ +dt=[0.5 .1 .001]; +figure(); +hold on + x=[0:dt(2):3]'; + y_n=zeros(size(x)); + y_n(1)=1; +for i=2:length(x) + dy=prob2_ode(x,y_n(i-1)); + y_n(i)=y_n(i-1)+ dt(2)*dy; +end +plot(x,exp(-x),x,y_n) +legend('Analytical','Euler','Location','Northeast') \ No newline at end of file diff --git a/prob2ptB.m b/prob2ptB.m index 4f336d6..43a380e 100644 --- a/prob2ptB.m +++ b/prob2ptB.m @@ -8,4 +8,5 @@ for i=2:length(x) dy=prob2_ode(x,y_n(i-1)); y_n(i)=y_n(i-1)+ dt(2)*dy; end -plot(x,exp(-x),'k-',x,y_n,'o'); \ No newline at end of file +plot(x,exp(-x),x,y_n) +legend('Analytical','Euler','Location','Northeast') \ No newline at end of file diff --git a/prob3plot.asv b/prob3plot.asv new file mode 100644 index 0000000..ca98161 --- /dev/null +++ b/prob3plot.asv @@ -0,0 +1,17 @@ +set(0, 'defaultAxesFontSize', 16) +set(0,'defaultTextFontSize',14) +set(0,'defaultLineLineWidth',1) +dt = 0.01; +t = [0:dt:3]; +y = zeros(length(t),2); +y(1,:) = [1,0]; +for i = 2:length(t) + dy = prob3_ode(t,y(i-1,:)); + y(i,:) = y(i-1,:)+dt*dy; +end +b = figure(2); +y_heun = prob3ptC (@(t,y) prob3_ode(t,y),0.01,[1,0],[0 3]); +plot(t,cos(3*t),t, y(:,1),t,y_heun(:,1)) +legend('Analytical','Euler','Heun','Location','Northeast') +xlabel('Time') +ylabel('Position') diff --git a/prob3plot.m b/prob3plot.m new file mode 100644 index 0000000..ca98161 --- /dev/null +++ b/prob3plot.m @@ -0,0 +1,17 @@ +set(0, 'defaultAxesFontSize', 16) +set(0,'defaultTextFontSize',14) +set(0,'defaultLineLineWidth',1) +dt = 0.01; +t = [0:dt:3]; +y = zeros(length(t),2); +y(1,:) = [1,0]; +for i = 2:length(t) + dy = prob3_ode(t,y(i-1,:)); + y(i,:) = y(i-1,:)+dt*dy; +end +b = figure(2); +y_heun = prob3ptC (@(t,y) prob3_ode(t,y),0.01,[1,0],[0 3]); +plot(t,cos(3*t),t, y(:,1),t,y_heun(:,1)) +legend('Analytical','Euler','Heun','Location','Northeast') +xlabel('Time') +ylabel('Position') diff --git a/prob3ptB.m b/prob3ptB.m index ee1e635..bdedc89 100644 --- a/prob3ptB.m +++ b/prob3ptB.m @@ -8,4 +8,5 @@ for i=2:length(x) dy=prob3_ode(x,y_n(i-1,:)); y_n(i,:)=y_n(i-1,:)+ dt(2)*dy; end -plot(x,cos(3*x),'k-',x,y_n(:,1),'o'); \ No newline at end of file +plot(x,cos(3*x),x,y_n(:,1)) +legend('Analytical','Euler','Location','Northeast') \ No newline at end of file diff --git a/prob3ptC.m b/prob3ptC.m new file mode 100644 index 0000000..201174c --- /dev/null +++ b/prob3ptC.m @@ -0,0 +1,20 @@ +function y = prob3ptC(prob3_ode, dt, y0,tlimits) + t = [tlimits(1):dt:tlimits(2)]; + y = zeros(length(t),length(y0)); + y(1,:) = y0; + for i = 2:length(t) + dy = prob3_ode(t(i-1),y(i-1,:)); + y(i,:) = y(i-1,:)+dt*dy; + dyc = (dy + prob3_ode(t(i),y(i,:)))/2; + y(i,:) = y(i-1,:)+dt*dyc; + n = 1; + while (1) + n = n+1; + yold = y(i,:); + dyc = (dy+prob3_ode(t(i),y(i,:)))/2; + y(i,:) = y(i-1,:)+dt*dyc; + ea = abs(y(i,:)- yold)./y(i,:)*100; + if max(ea) < 0.0001 || n>100; break, end + end + end +end \ No newline at end of file