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Mariusz Iwaniuk

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Use assuming....

Mariusz Iwaniuk 1571
June 11 2018
0 0

@digerdiga 

`assuming`([convert(signum(0, R-sqrt(R^2+z^2), 1), piecewise)], [R-sqrt(R^2+z^2) < 0]);

# -1

or:

`assuming`([signum(0, R-sqrt(R^2+z^2), 1)], [R-sqrt(R^2+z^2) < 0])

#-1

Maple have some limitation about regarding the resolution of the case and falsehood.

restart:

assume(R > 0, z > 0, R in real, z in real);

coulditbe(R-sqrt(R^2+z^2) < 0);#FAIL

is(R-sqrt(R^2+z^2) < 0);#FAIL

....

Mariusz Iwaniuk 1571
June 10 2018
0 0

Maybe this helps: http://www.cim.mcgill.ca/~migueltt/ltp/ltp.html

From Wikipedia......

Mariusz Iwaniuk 1571
June 09 2018
0 0

@one pound 

From Wikipedia, using property: Ei(1,z) = - Ei(-z) and faster converging series by Ramanujan:

For example, for z = 10,and for  40 terms  an answer correct to 16 significant figures.

series.mw

Check....

Mariusz Iwaniuk 1571
June 04 2018
0 0

@kuwait1 

A numeric check gives a big numbers in domain x=(-5,5) and z=(-5,5).Integral is divergent.

r := 2.5;
Q := proc (x, z) options operator, arrow; evalf(Int(1/(x*r^2*cos(x-y)+z*r^2*sin(z-y))^5, y = 0 .. Pi, method = _Gquad, epsilon = 1/100000)) end proc;
seq(seq(lprint(Q(x, z)), x = -5 .. 5, .25), z = -5 .. 5, .25);

-0.3091653839e55
0.7846201518e57
0.2353821795e58
-0.7841865263e57
-0.7756899663e57
0.1123370081e58
...

....

Mariusz Iwaniuk 1571
May 31 2018
0 0

@ssllys You are welcome :)

....

Mariusz Iwaniuk 1571
May 31 2018
0 0

@mmcdara . Thanks for checking :)

Works on Maple 2017.3 and 2018....

Mariusz Iwaniuk 1571
May 31 2018
0 0

@pr0t3ctabl3 

All  my code in answer works on Maple 2017.3 and 2018. I don't have earlier version of Maple, so I will not check it.

....

Mariusz Iwaniuk 1571
May 31 2018
0 0

@pr0t3ctabl3 

I edited the answer.It should work now.

All code was exectuted in Maple 2018.

Article:...

Mariusz Iwaniuk 1571
May 31 2018
0 0

@mmcdara 

31165-118782-3-PB.pdf

By googling...

Mariusz Iwaniuk 1571
May 30 2018
0 0

 look here: https://www.mapleprimes.com/questions/147800-Code-For-Homotopy-Analysis-Method and choose what you need.

If you discovered a strange result produ...

Mariusz Iwaniuk 1571
May 25 2018
0 0

If you discovered a strange result produced by Maple,
it would be useful to exhibit the simplest version where
this abnormal result is still present.Can you add actual code so people can copy-paste easily?.

....

Mariusz Iwaniuk 1571
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 1571
May 19 2018
0 0

Thanks.@Carl Love 

....

Mariusz Iwaniuk 1571
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 1571
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.

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