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....

Mariusz Iwaniuk 1643
May 20 2018
0 0

@Gabriel samaila 


 

> 

restart
> 

H[a] := 5; P[m] := .8; V[0] := 1; N[b] := .1; P[r] := 10; N[t] := .1; B[r] := 1; S[c] := 1

5

  

.8

  

1

  

.1

  

10

  

.1

  

1

  

1

 (1)
> 

dsys := {diff(x[1](y), y) = 1, diff(x[2](y), y) = x[3](y), diff(x[3](y), y) = -x[6](y)-H[a]*x[3](y)-V[0]*x[3](y)-B[r]*x[8](y), diff(x[4](y), y) = x[5](y), diff(x[5](y), y) = -H[a]*P[m]*x[3](y)-V[0]*P[m]*x[5](y), diff(x[6](y), y) = x[7](y), diff(x[7](y), y) = -N[t]*x[7](y)^2-V[0]*P[r]*x[7](y)-N[b]*x[7](y)*x[9](y), diff(x[8](y), y) = x[9](y), diff(x[9](y), y) = -V[0]*S[c]*x[9](y)+N[t]^2*x[7](y)^2/N[b]+N[t]*P[r]*x[7](y)/N[b]+N[t]*x[7](y)*x[9](y), x[1](0) = 0, x[2](0) = 0, x[3](0) = 0, x[4](0) = 0, x[5](0) = 0, x[6](0) = 0, x[7](0) = -1, x[8](0) = 1, x[9](0) = -.68}

{diff(x[1](y), y) = 1, diff(x[2](y), y) = x[3](y), diff(x[3](y), y) = -x[6](y)-6*x[3](y)-x[8](y), diff(x[4](y), y) = x[5](y), diff(x[5](y), y) = -4.0*x[3](y)-.8*x[5](y), diff(x[6](y), y) = x[7](y), diff(x[7](y), y) = -.1*x[7](y)^2-10*x[7](y)-.1*x[7](y)*x[9](y), diff(x[8](y), y) = x[9](y), diff(x[9](y), y) = -x[9](y)+.1000000000*x[7](y)^2+10.00000000*x[7](y)+.1*x[7](y)*x[9](y), x[1](0) = 0, x[2](0) = 0, x[3](0) = 0, x[4](0) = 0, x[5](0) = 0, x[6](0) = 0, x[7](0) = -1, x[8](0) = 1, x[9](0) = -.68}

 (2)
> 

sol := dsolve(dsys, numeric, method = classical[rk4], stepsize = .1)

proc (x_classical) local _res, _dat, _vars, _solnproc, _xout, _ndsol, _pars, _n, _i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; if 1 < nargs then error "invalid input: too many arguments" end if; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then _xout := evalf[_EnvDSNumericSaveDigits](x_classical) else _xout := evalf(x_classical) end if; _dat := Array(1..4, {(1) = proc (_xin) local _xout, _n, _y0, _yn, _yl, _ctl, _octl, _reinit, _errcd, _fcn, _i, _yini, _pars, _ini, _par; option `Copyright (c) 2002 by the University of Waterloo. All rights reserved.`; table( [( "complex" ) = false ] ) _xout := _xin; _ctl := Array(1..9, {(1) = 9, (2) = 0., (3) = 0., (4) = .1, (5) = 50000, (6) = 0, (7) = 4, (8) = 1, (9) = 0}); _octl := Array(1..9, {(1) = 9, (2) = 0., (3) = 0., (4) = .1, (5) = 50000, (6) = 0, (7) = 4, (8) = 1, (9) = 0}); _n := trunc(_ctl[1]); _yini := Array(0..9, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0., (6) = 0., (7) = 0., (8) = -1., (9) = 1.}); _y0 := Array(0..9, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0., (6) = 0., (7) = 0., (8) = -1., (9) = 1.}); _yl := Array(1..9, {(1) = 0, (2) = 0, (3) = 0, (4) = 0, (5) = 0, (6) = 0, (7) = 0, (8) = 0, (9) = 0}); _yn := Array(1..9, {(1) = 0, (2) = 0, (3) = 0, (4) = 0, (5) = 0, (6) = 0, (7) = 0, (8) = 0, (9) = 0}); _fcn := proc (N, X, Y, YP) option `[Y[1] = x[1](y), Y[2] = x[2](y), Y[3] = x[3](y), Y[4] = x[4](y), Y[5] = x[5](y), Y[6] = x[6](y), Y[7] = x[7](y), Y[8] = x[8](y), Y[9] = x[9](y)]`; YP[1] := 1; YP[3] := -Y[6]-6*Y[3]-Y[8]; YP[5] := -4.0*Y[3]-.8*Y[5]; YP[7] := -.1*Y[7]^2-10*Y[7]-.1*Y[7]*Y[9]; YP[9] := -Y[9]+.1000000000*Y[7]^2+10.00000000*Y[7]+.1*Y[7]*Y[9]; YP[2] := Y[3]; YP[4] := Y[5]; YP[6] := Y[7]; YP[8] := Y[9]; 0 end proc; _pars := []; if not type(_xout, 'numeric') then if member(_xout, ["start", "left", "right"]) then return _y0[0] elif _xout = "method" then return "classical" elif _xout = "numfun" then return round(_ctl[6]) elif _xout = "initial" then return [seq(_yini[_i], _i = 0 .. _n)] elif _xout = "parameters" then return [seq(_yini[_n+_i], _i = 1 .. nops(_pars))] elif _xout = "initial_and_parameters" then return [seq(_yini[_i], _i = 0 .. _n)], [seq(_yini[_n+_i], _i = 1 .. nops(_pars))] elif _xout = "last" then if _ctl[3]-_y0[0] <> 0. then _xout := _ctl[3] elif _ctl[2]-_y0[0] <> 0. then _xout := _ctl[2] else error "no information is available on last computed point" end if elif _xout = "enginedata" then return eval(_octl, 1) elif _xout = "function" then return eval(_fcn, 1) elif type(_xin, `=`) and type(rhs(_xin), 'list') and member(lhs(_xin), {"initial", "parameters", "initial_and_parameters"}) then _ini, _par := [], []; if lhs(_xin) = "initial" then _ini := rhs(_xin) elif lhs(_xin) = "parameters" then _par := rhs(_xin) elif select(type, rhs(_xin), `=`) <> [] then _par, _ini := selectremove(type, rhs(_xin), `=`) elif nops(rhs(_xin)) < nops(_pars)+1 then error "insufficient data for specification of initial and parameters" else _par := rhs(_xin)[-nops(_pars) .. -1]; _ini := rhs(_xin)[1 .. -nops(_pars)-1] end if; _xout := lhs(_xout); if _par <> [] then `dsolve/numeric/process_parameters`(_n, _pars, _par, _yini) end if; if _ini <> [] then `dsolve/numeric/process_initial`(_n, _ini, _yini, _pars) end if; if _pars <> [] then _par := {seq(rhs(_pars[_i]) = _yini[_n+_i], _i = 1 .. nops(_pars))}; for _i from 0 to _n do _y0[_i] := subs(_par, _yini[_i]) end do; for _i from _n+1 to _n+nops(_pars) do _y0[_i] := _yini[_i] end do; for _i to nops(_pars) do _yn[_n+_i] := _y0[_n+_i] end do else for _i from 0 to _n do _y0[_i] := _yini[_i] end do end if; _octl[2] := _y0[0]; _octl[3] := _y0[0]; for _i to 9 do _ctl[_i] := _octl[_i] end do; for _i to _n+nops(_pars) do _yl[_i] := _y0[_i] end do; if _Env_smart_dsolve_numeric = true and type(_y0[0], 'numeric') then procname("right") := _y0[0]; procname("left") := _y0[0] end if; if _xout = "initial" then return [seq(_yini[_i], _i = 0 .. _n)] elif _xout = "parameters" then return [seq(_yini[_n+_i], _i = 1 .. nops(_pars))] else return [seq(_yini[_i], _i = 0 .. _n), op(_pars)], [seq(_yini[_n+_i], _i = 1 .. nops(_pars))] end if else return "procname" end if end if; if _xout-_y0[0] = 0. then return [seq(_y0[_i], _i = 0 .. _n)] end if; _reinit := false; if _xin <> "last" then if 0 < 0 and `dsolve/numeric/checkglobals`(0, table( [ ] ), _pars, _n, _yini) then _reinit := true; if _pars <> [] then _par := {seq(rhs(_pars[_i]) = _yini[_n+_i], _i = 1 .. nops(_pars))}; for _i from 0 to _n do _y0[_i] := subs(_par, _yini[_i]) end do; for _i from _n+1 to _n+nops(_pars) do _y0[_i] := _yini[_i] end do; for _i to nops(_pars) do _yn[_n+_i] := _y0[_n+_i] end do else for _i from 0 to _n do _y0[_i] := _yini[_i] end do end if end if; if _pars <> [] and select(type, {seq(_yini[_n+_i], _i = 1 .. nops(_pars))}, 'undefined') <> {} then error "parameters must be initialized before solution can be computed" end if end if; if not _reinit and _xout-_ctl[3] = 0. then [_ctl[3], seq(_yn[_i], _i = 1 .. _n)] elif not _reinit and _xout-_ctl[2] = 0. then [_ctl[2], seq(_yl[_i], _i = 1 .. _n)] else if _ctl[2]-_y0[0] = 0. or sign(_ctl[2]-_y0[0]) <> sign(_xout-_ctl[2]) or abs(_xout-_y0[0]) < abs(_xout-_ctl[2]) or _reinit then for _i to 9 do _ctl[_i] := _octl[_i] end do; for _i to _n+nops(_pars) do _yl[_i] := _y0[_i] end do; for _i to nops(_pars) do _yn[_n+_i] := _y0[_n+_i] end do end if; _ctl[3] := _xout; if Digits <= evalhf(Digits) then try _errcd := evalhf(`dsolve/numeric/classical`(_fcn, var(_ctl), _y0[0], var(_yl), var(_yn), Array(1..9, {(1) = 0, (2) = 0, (3) = 0, (4) = 0, (5) = 0, (6) = 0, (7) = 0, (8) = 0, (9) = 0}), Array(1..9, {(1) = 0, (2) = 0, (3) = 0, (4) = 0, (5) = 0, (6) = 0, (7) = 0, (8) = 0, (9) = 0}), Array(1..9, {(1) = 0, (2) = 0, (3) = 0, (4) = 0, (5) = 0, (6) = 0, (7) = 0, (8) = 0, (9) = 0}), Array(1..9, {(1) = 0, (2) = 0, (3) = 0, (4) = 0, (5) = 0, (6) = 0, (7) = 0, (8) = 0, (9) = 0}), var(Array(1..3, 1..9, {(1, 1) = 0, (1, 2) = 0, (1, 3) = 0, (1, 4) = 0, (1, 5) = 0, (1, 6) = 0, (1, 7) = 0, (1, 8) = 0, (1, 9) = 0, (2, 1) = 0, (2, 2) = 0, (2, 3) = 0, (2, 4) = 0, (2, 5) = 0, (2, 6) = 0, (2, 7) = 0, (2, 8) = 0, (2, 9) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = 0, (3, 4) = 0, (3, 5) = 0, (3, 6) = 0, (3, 7) = 0, (3, 8) = 0, (3, 9) = 0})))) catch: userinfo(2, `dsolve/debug`, print(`Exception in classical:`, [lastexception])); if searchtext('evalhf', lastexception[2]) <> 0 or searchtext('real', lastexception[2]) <> 0 or searchtext('hardware', lastexception[2]) <> 0 then _errcd := `dsolve/numeric/classical`(_fcn, _ctl, _y0[0], _yl, _yn, Array(1..9, {(1) = 0, (2) = 0, (3) = 0, (4) = 0, (5) = 0, (6) = 0, (7) = 0, (8) = 0, (9) = 0}), Array(1..9, {(1) = 0, (2) = 0, (3) = 0, (4) = 0, (5) = 0, (6) = 0, (7) = 0, (8) = 0, (9) = 0}), Array(1..9, {(1) = 0, (2) = 0, (3) = 0, (4) = 0, (5) = 0, (6) = 0, (7) = 0, (8) = 0, (9) = 0}), Array(1..9, {(1) = 0, (2) = 0, (3) = 0, (4) = 0, (5) = 0, (6) = 0, (7) = 0, (8) = 0, (9) = 0}), Array(1..3, 1..9, {(1, 1) = 0, (1, 2) = 0, (1, 3) = 0, (1, 4) = 0, (1, 5) = 0, (1, 6) = 0, (1, 7) = 0, (1, 8) = 0, (1, 9) = 0, (2, 1) = 0, (2, 2) = 0, (2, 3) = 0, (2, 4) = 0, (2, 5) = 0, (2, 6) = 0, (2, 7) = 0, (2, 8) = 0, (2, 9) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = 0, (3, 4) = 0, (3, 5) = 0, (3, 6) = 0, (3, 7) = 0, (3, 8) = 0, (3, 9) = 0})) else _ctl[3] := _y0[0]; _errcd := [lastexception][2 .. -1] end if end try else try _errcd := `dsolve/numeric/classical`(_fcn, _ctl, _y0[0], _yl, _yn, Array(1..9, {(1) = 0, (2) = 0, (3) = 0, (4) = 0, (5) = 0, (6) = 0, (7) = 0, (8) = 0, (9) = 0}), Array(1..9, {(1) = 0, (2) = 0, (3) = 0, (4) = 0, (5) = 0, (6) = 0, (7) = 0, (8) = 0, (9) = 0}), Array(1..9, {(1) = 0, (2) = 0, (3) = 0, (4) = 0, (5) = 0, (6) = 0, (7) = 0, (8) = 0, (9) = 0}), Array(1..9, {(1) = 0, (2) = 0, (3) = 0, (4) = 0, (5) = 0, (6) = 0, (7) = 0, (8) = 0, (9) = 0}), Array(1..3, 1..9, {(1, 1) = 0, (1, 2) = 0, (1, 3) = 0, (1, 4) = 0, (1, 5) = 0, (1, 6) = 0, (1, 7) = 0, (1, 8) = 0, (1, 9) = 0, (2, 1) = 0, (2, 2) = 0, (2, 3) = 0, (2, 4) = 0, (2, 5) = 0, (2, 6) = 0, (2, 7) = 0, (2, 8) = 0, (2, 9) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = 0, (3, 4) = 0, (3, 5) = 0, (3, 6) = 0, (3, 7) = 0, (3, 8) = 0, (3, 9) = 0})) catch: _ctl[3] := _y0[0]; _errcd := [lastexception][2 .. -1] end try end if; if type(_errcd, 'list') or _errcd < 0 then userinfo(2, {dsolve, `dsolve/classical`}, `Last values returned:`); userinfo(2, {dsolve, `dsolve/classical`}, ` t =`, _ctl[2]); userinfo(2, {dsolve, `dsolve/classical`}, ` y =`, _yl[1]); for _i from 2 to _n do userinfo(2, {dsolve, `dsolve/classical`}, ` `, _yl[_i]) end do; if type(_errcd, 'list') then error op(_errcd) elif _errcd+1. = 0. then Rounding := `if`(_y0[0] < _xout, -infinity, infinity); error "cannot evaluate the solution past %1, maxfun limit exceeded (see ?dsolve,maxfun for details)", evalf[8](_ctl[3]) else Rounding := `if`(_y0[0] < _xout, -infinity, infinity); error "cannot evaluate the solution past %1, unknown error code returned from classical %2", evalf[8](_ctl[3]), trunc(_errcd) end if end if; if _Env_smart_dsolve_numeric = true then if _y0[0] < _xout and procname("right") < _xout then procname("right") := _xout elif _xout < _y0[0] and _xout < procname("left") then procname("left") := _xout end if end if; [_xout, seq(_yn[_i], _i = 1 .. _n)] end if end proc, (2) = Array(0..0, {}), (3) = [y, x[1](y), x[2](y), x[3](y), x[4](y), x[5](y), x[6](y), x[7](y), x[8](y), x[9](y)], (4) = []}); _vars := _dat[3]; _pars := map(rhs, _dat[4]); _n := nops(_vars)-1; _solnproc := _dat[1]; if not type(_xout, 'numeric') then if member(x_classical, ["start", 'start', "method", 'method', "left", 'left', "right", 'right', "leftdata", "rightdata", "enginedata", "eventstop", 'eventstop', "eventclear", 'eventclear', "eventstatus", 'eventstatus', "eventcount", 'eventcount', "laxtol", 'laxtol', "numfun", 'numfun', NULL]) then _res := _solnproc(convert(x_classical, 'string')); if 1 < nops([_res]) then return _res elif type(_res, 'array') then return eval(_res, 1) elif _res <> "procname" then return _res end if elif member(x_classical, ["last", 'last', "initial", 'initial', "parameters", 'parameters', "initial_and_parameters", 'initial_and_parameters', NULL]) then _xout := convert(x_classical, 'string'); _res := _solnproc(_xout); if _xout = "parameters" then return [seq(_pars[_i] = _res[_i], _i = 1 .. nops(_pars))] elif _xout = "initial_and_parameters" then return [seq(_vars[_i+1] = [_res][1][_i+1], _i = 0 .. _n), seq(_pars[_i] = [_res][2][_i], _i = 1 .. nops(_pars))] else return [seq(_vars[_i+1] = _res[_i+1], _i = 0 .. _n)] end if elif type(_xout, `=`) and member(lhs(_xout), ["initial", 'initial', "parameters", 'parameters', "initial_and_parameters", 'initial_and_parameters', NULL]) then _xout := convert(lhs(x_classical), 'string') = rhs(x_classical); if type(rhs(_xout), 'list') then _res := _solnproc(_xout) else error "initial and/or parameter values must be specified in a list" end if; if lhs(_xout) = "initial" then return [seq(_vars[_i+1] = _res[_i+1], _i = 0 .. _n)] elif lhs(_xout) = "parameters" then return [seq(_pars[_i] = _res[_i], _i = 1 .. nops(_pars))] else return [seq(_vars[_i+1] = [_res][1][_i+1], _i = 0 .. _n), seq(_pars[_i] = [_res][2][_i], _i = 1 .. nops(_pars))] end if elif type(_xout, `=`) and member(lhs(_xout), ["eventdisable", 'eventdisable', "eventenable", 'eventenable', "eventfired", 'eventfired', "direction", 'direction', NULL]) then return _solnproc(convert(lhs(x_classical), 'string') = rhs(x_classical)) elif _xout = "solnprocedure" then return eval(_solnproc) elif _xout = "sysvars" then return _vars end if; if procname <> unknown then return ('procname')(x_classical) else _ndsol := 1; _ndsol := _ndsol; _ndsol := pointto(_dat[2][0]); return ('_ndsol')(x_classical) end if end if; try _res := _solnproc(_xout); [seq(_vars[_i+1] = _res[_i+1], _i = 0 .. _n)] catch: error end try end proc

 (3)
> 

plots:-odeplot(sol, [[y, x[8](y)]], y = 0 .. 2, color = ["Red"])

 
> 

plots:-odeplot(sol, [seq([y, x[j](y)], j = 1 .. 8)], y = 0 .. 2, view = [0 .. 2, -1 .. 1], color = ["Red", "Blue", "Black", "Green", "Yellow", "Pink", "Nautical GrayViolet", "Niagara DarkOrchid"])

 
> 

``


 

Download testODE2.mw

 

Your_Way.mw

Done....

Mariusz Iwaniuk 1643
May 19 2018
0 0

Thanks.@Carl Love 

....

Mariusz Iwaniuk 1643
May 18 2018
0 0

I wrote a code example here, because You don't give any. I not a Harry Potter to see and reads OP's  code minds.
Download PDESOL.mw

Everything is missing......

Mariusz Iwaniuk 1643
May 18 2018
0 0

People here generally like users to post code as Maple code instead of images or TeX, so they can copy-paste it. It makes it convenient for them and more likely you will get someone to help you. You want solve PDE numerically then add the missing parameters,like initial,boundary conditions,concentration of electrons and so on.

:)...

Mariusz Iwaniuk 1643
May 17 2018
0 0

thanks a lot@Kitonum 

....

Mariusz Iwaniuk 1643
May 17 2018
0 0

@Kitonum 

Binary(4);

convert(4, base, 2);#Check

                           [1, 0, 0]
                           [0, 0, 1] ?
 

....

Mariusz Iwaniuk 1643
May 17 2018
0 0

Maybe this help you:https://www.mapleprimes.com/questions/203465-How-Do-I-WRITE-not-convert-To-A

....

Mariusz Iwaniuk 1643
May 17 2018
0 0

 Maple does not give any solution because No solution exist in yours case.

FAIL....

Mariusz Iwaniuk 1643
May 17 2018

Mathematica 11.3 can't compute limit (2) too.

....

Mariusz Iwaniuk 1643
May 13 2018
0 0

@acer 

Thanks. Exactly that's what I needed.

....

Mariusz Iwaniuk 1643
May 12 2018
0 0

@vv 

Thank you very much. :)

....

Mariusz Iwaniuk 1643
May 12 2018
0 0

@vv 

Thanks,but:

plot([f, 'fdiff(f(t), t = x)'], x = 0 .. 10);# Not working ?

plot([f, 'fdiff(f(t), t = x)'], 0 .. 10);# Not working ?

 

How to do it on  the one plot  not using a display command.? 

....

Mariusz Iwaniuk 1643
May 12 2018
0 0

@Kitonum 

Thanks ,but i need  solution of my problem with new Interpolation[Interpolate] packges.

No exist....

Mariusz Iwaniuk 1643
May 10 2018
0 0

Probably exact solution no exist. With Maple 2018 and updated version Physics package version 39 ,Maple return NULL.

Mathematica 11.3 also does not know the answer.

No-PDE_exact.mw

PDE Mathematica.pdf

 

....

Mariusz Iwaniuk 1643
May 09 2018
0 0

@ecterrab 

Ok thank for the explanation.

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