## [Maxima-commits] CVS: maxima/share/orthopoly variational_method.dem,1.2,1.3

 [Maxima-commits] CVS: maxima/share/orthopoly variational_method.dem,1.2,1.3 From: Barton Willis - 2005-12-23 13:47:08 ```Update of /cvsroot/maxima/maxima/share/orthopoly In directory sc8-pr-cvs1.sourceforge.net:/tmp/cvs-serv8375/share/orthopoly Modified Files: variational_method.dem Log Message: (1) added non-pertrubative solver (2) appended cleanup code Index: variational_method.dem =================================================================== RCS file: /cvsroot/maxima/maxima/share/orthopoly/variational_method.dem,v retrieving revision 1.2 retrieving revision 1.3 diff -u -d -r1.2 -r1.3 --- variational_method.dem 14 Dec 2005 18:57:50 -0000 1.2 +++ variational_method.dem 23 Dec 2005 13:46:58 -0000 1.3 @@ -12,7 +12,7 @@ assign a value to n, load orthopoly, and assign psi. */ -n : 4; +n : 3; if get('orthopoly,'version) = 'false then load("orthopoly")\$ @@ -55,7 +55,7 @@ mu = cf[ 0] + cf[1] * epsilon + ... + cf[solve_ord] epsilon^solve_ord. */ -solve_ord : 5; +solve_ord : 3; pows : makelist(epsilon^i,i,0,solve_ord)\$ unks : makelist(cf[ i ],i,0,solve_ord)\$ eq : ev(m_det, mu = unks . pows)\$ @@ -65,13 +65,27 @@ ans : algsys(eq, unks)\$ for i : 1 thru length(ans) do ( - ans[ i ] : map(rhs, ans[ i ]) . pows -)\$ + ans[ i ] : map(rhs, ans[ i ]) . pows)\$ -/* Look at the solution graphically. Plotting might be really slow -*/ +ans : reverse(ans); -ans; - -plot2d(ans, [epsilon,0,0.15],[y,0,30]); +/* Look at the solution graphically.*/ + +plot2d(ans, [epsilon,0,0.25]); +/* Let's solve the equations using allroots instead of the series method. */ + +f(x,k) := part(sort(map('rhs, allroots(subst('epsilon=x,m_det)))),k); + +/* Compare the allroots solution to the series solution. */ + +plot2d([ans[1], '(f(epsilon,1))], [epsilon,0.0,0.4]); +plot2d([ans[2], '(f(epsilon,2))], [epsilon,0.0,0.4]); +plot2d([ans[3], '(f(epsilon,3))], [epsilon,0.0,0.4]); +plot2d([ans[4], '(f(epsilon,4))], [epsilon,0.0,0.4]); + +plot2d(['(f(epsilon,1)),'(f(epsilon,2)),'(f(epsilon,3)),'(f(epsilon,4))],[epsilon,0,0.4]); + +remfunction(ham,"<<",f); +remvalue(n,psi,vars,min_this,eqs,m_det,solve_ord,pows,unks,eq,ans); +assume_pos : false; ```

 [Maxima-commits] CVS: maxima/share/orthopoly variational_method.dem,1.2,1.3 From: Barton Willis - 2005-12-23 13:47:08 ```Update of /cvsroot/maxima/maxima/share/orthopoly In directory sc8-pr-cvs1.sourceforge.net:/tmp/cvs-serv8375/share/orthopoly Modified Files: variational_method.dem Log Message: (1) added non-pertrubative solver (2) appended cleanup code Index: variational_method.dem =================================================================== RCS file: /cvsroot/maxima/maxima/share/orthopoly/variational_method.dem,v retrieving revision 1.2 retrieving revision 1.3 diff -u -d -r1.2 -r1.3 --- variational_method.dem 14 Dec 2005 18:57:50 -0000 1.2 +++ variational_method.dem 23 Dec 2005 13:46:58 -0000 1.3 @@ -12,7 +12,7 @@ assign a value to n, load orthopoly, and assign psi. */ -n : 4; +n : 3; if get('orthopoly,'version) = 'false then load("orthopoly")\$ @@ -55,7 +55,7 @@ mu = cf[ 0] + cf[1] * epsilon + ... + cf[solve_ord] epsilon^solve_ord. */ -solve_ord : 5; +solve_ord : 3; pows : makelist(epsilon^i,i,0,solve_ord)\$ unks : makelist(cf[ i ],i,0,solve_ord)\$ eq : ev(m_det, mu = unks . pows)\$ @@ -65,13 +65,27 @@ ans : algsys(eq, unks)\$ for i : 1 thru length(ans) do ( - ans[ i ] : map(rhs, ans[ i ]) . pows -)\$ + ans[ i ] : map(rhs, ans[ i ]) . pows)\$ -/* Look at the solution graphically. Plotting might be really slow -*/ +ans : reverse(ans); -ans; - -plot2d(ans, [epsilon,0,0.15],[y,0,30]); +/* Look at the solution graphically.*/ + +plot2d(ans, [epsilon,0,0.25]); +/* Let's solve the equations using allroots instead of the series method. */ + +f(x,k) := part(sort(map('rhs, allroots(subst('epsilon=x,m_det)))),k); + +/* Compare the allroots solution to the series solution. */ + +plot2d([ans[1], '(f(epsilon,1))], [epsilon,0.0,0.4]); +plot2d([ans[2], '(f(epsilon,2))], [epsilon,0.0,0.4]); +plot2d([ans[3], '(f(epsilon,3))], [epsilon,0.0,0.4]); +plot2d([ans[4], '(f(epsilon,4))], [epsilon,0.0,0.4]); + +plot2d(['(f(epsilon,1)),'(f(epsilon,2)),'(f(epsilon,3)),'(f(epsilon,4))],[epsilon,0,0.4]); + +remfunction(ham,"<<",f); +remvalue(n,psi,vars,min_this,eqs,m_det,solve_ord,pows,unks,eq,ans); +assume_pos : false; ```