salauayobami

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MaplePrimes Activity


These are replies submitted by salauayobami

I am finding it hard to upload the file using the upload button

@Carl Love 

I do like to see the shooting method with RKF45 as the underlying IVP

Thanks.

@Carl Love is there a way u can help show that using the above code and question? Thanks

is it a flow problem, and what method do you intend to use?

@tomleslie is the solution provided by you RKF45 or is it still FDM

you can solve this ODE by using the Inbuilt Maple ODE solver, first you type in the ODE in question as an input, then press enter and highlight the output and right click to get options and then click solve ode.

and i deleted the d in the first ODE and i got another error

SOL := dsolve({bc, subs(parameter, ODE1), subs(parameter, ODE2), subs(parameter, ODE3)}, type = numeric);

gives the below error
Error, (in Fproc) invalid input: diff received HFloat(6.0), which is not valid for its 2nd argument


 

restart

NULL

fw := fw; M := M; R := R; N := N; a := a; m := m; Ec := Ec; Pr := Pr; d := d; l := l

fw

 

M

 

R

 

N

 

a

 

m

 

Ec

 

Pr

 

d

 

l

(1)

Digits := 30

30

(2)

Setup*of*BVP*system

ODEs := [diff(f(eta), `$`(eta, 3))-a*(diff(theta(eta), eta))*(diff(f(eta), `$`(eta, 2)))/(a*theta(eta)+1)+(a*theta(eta)+1)*M*(1-(diff(f(eta), eta)))+(a*theta(eta)+1)*m*(1-(diff(f(eta), eta))^2)+(a*theta(eta)+1)*f(eta)*(diff(f(eta), `$`(eta, 2)))*((m+1)*(1/2))+(a*theta(eta)+1)*d*theta(eta), (l*(diff(theta(eta), eta))^2*N*(gamma*theta(eta)+1)^(N-1)+(diff(theta(eta), `$`(eta, 2)))*(l*theta(eta)+1)^N+(4/3)*R*(diff(theta(eta), `$`(eta, 2))))/Pr+Ec*(diff(f(eta), eta))^2+M*Ec*(1-(diff(f(eta), eta)))^2-(diff(f(eta), eta))*theta(eta)*(2*m-1)+(diff(theta(eta), eta))*((m+1)*(1/2))*f(eta)]; `<,>`(ODEs[])

Vector[column](%id = 36893490908558672588)

(3)

LB, UB := 0, infinity; BCs := [`~`[`=`](([f, D(f), D(theta)])(LB), [fw, epsilon+delta*D@@2*f, -1])[], `~`[`=`](([D(f), theta])(UB), [1, 0])[]]

[f(0) = fw, (D(f))(0) = varepsilon+delta*D@@2*f, (D(theta))(0) = -1, (D(f))(infinity) = 1, theta(infinity) = 0]

(4)

Params := Record(a = 1, Pr = 1, Ec = 1, delta = 1, m = 1, M = 1, N = 1, R = 1, d = 1, l = 1, fw = 1, epsilon = 1)

NBVs := [-((D@@2)(f))(1) = `C*__f`, -(D(theta))(1) = `Nu*`]; Nu := `Nu*`; Cf := `C*__f`

Solve := module () local nbvs_rhs, Sol, ModuleApply, AccumData, ModuleLoad; export SavedData, Pos, Init;  nbvs_rhs := `~`[rhs](:-NBVs); ModuleApply := subs(_Sys = {:-BCs[], :-ODEs[]}, proc ({ a::realcons := Params:-a, Pr::realcons := Params:-Pr, Ec::realcons := Params:-Ec, delta::realcons := Params:-delta, m::realcons := Params:-m, M::realcons := Params:-M, N::realcons := Params:-N, R::realcons := Params:-R, d::realcons := Params:-d, l::realcons := Params:-l, fw::realcons := Params:-fw, epsilon::realcons := Params:-epsilon }) Sol := dsolve(_Sys, _rest, numeric, method = bvp[middefer], output = listprocedure, abserr = 0.1e3); AccumData(Sol, {_options}); Sol end proc); AccumData := proc (Sol::{Matrix, procedure, list({name, function} = procedure)}, params::(set(name = realcons))) local n, nbvs; if Sol::Matrix then nbvs := seq(n = Sol[2, 1][1, Pos(n)], n = nbvs_rhs) else nbvs := `~`[`=`](nbvs_rhs, eval(nbvs_rhs, Sol(:-UB)))[] end if; SavedData[params] := Record[packed](params[], nbvs) end proc; ModuleLoad := eval(Init); Init := proc () Pos := proc (n::name) local p; option remember; member(n, Sol[0, 1], 'p'); p end proc; SavedData := table(); return  end proc; ModuleLoad() end module

colseq := [red, green, blue]

Pc := Ec = 1, Pr = 1

Ps := [[Ec = 1, Pr = 1, m = 1, R = 1, N = 1, a = 1, l = 1, delta = 1], [Ec = 1, Pr = 1, m = 1, M = 1, fw = 1, N = 1, epsilon = 1, a = 1, l = 1, delta = 1], [Ec = 1, Pr = 1, m = 1, M = 1, fw = 1, R = 1, epsilon = 1, a = 1, l = 1, delta = 1]]; Pv := [M = [1, 2, 3], R = [0, 1, 2], N = [0, 1, 2]]

for i to nops(Ps) do plots:-display([seq(plots:-odeplot(Solve(lhs(Pv[i]) = rhs(Pv[i])[j], Ps[i][], Pc), [eta, theta(eta)], 'color' = colseq[j], 'legend' = [lhs(Pv[i]) = rhs(Pv[i])[j]]), j = 1 .. nops(rhs(Pv[i])))], 'axes' = 'boxed', 'gridlines' = false, 'labelfont' = ['TIMES', 'BOLDOBLIQUE', 16], 'caption' = nprintf(cat(`$`("\n%a = %4.2f, ", nops(Ps[i])-1), "%a = %4.2f\n\n"), `~`[lhs, rhs](Ps[i])[]), 'captionfont' = ['TIMES', 16]) end do

Error, (in dsolve/numeric/bvp/convertsys) too few boundary conditions: expected 7, got 5

 

Ps := [[Ec = 1, Pr = 1, m = 1.5, R = 1, fw = 1, N = 1, epsilon = .5, a = 1, l = .5, delta = 1], [Ec = 1, Pr = 1, m = 1.5, M = 1, fw = 1, N = 1, epsilon = .5, a = 1, l = 1, delta = 1], [Ec = 5, Pr = 1, m = 2, M = 1, fw = 1, R = 1, epsilon = 1, a = 1, l = 1, delta = 1]]; Pq := [d = [1, -.5], d = [1, -.5], d = [1, -.5]]

NULL

NULL

for i to nops(Ps) do plots:-display([seq(plots:-odeplot(Solve(lhs(Pq[i]) = rhs(Pq[i])[j], Ps[i][], Pc), [eta, theta(eta)], 'color' = colseq[j], 'legend' = [lhs(Pq[i]) = rhs((Pq, Pv)[i])[j]]), j = 1 .. nops(rhs(Pq[i])))], 'axes' = 'boxed', 'gridlines' = false, 'labelfont' = ['TIMES', 'BOLDOBLIQUE', 16], 'caption' = nprintf(cat(`$`("\n%a = %4.2f, ", nops(Ps[i])-1), "%a = %4.2f\n\n"), `~`[lhs, rhs](Ps[i])[]), 'captionfont' = ['TIMES', 16]) end do

Error, (in dsolve/numeric/bvp/convertsys) too few boundary conditions: expected 7, got 5

 

NULL

NULL

NULL

NULL

NULL

NULL

NULL

NULL


 

Download ADM_GRAPH_PROJ.mw

this is the code attached

@Carl Love  can you please help check this code, it's saying Error, (in dsolve/numeric/bvp/convertsys) too few boundary conditions: expected 7, got 5

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