torabi

Thanks for your attention. If there is an error in input data, but the appearance of the graph should be similar, though with different data. Also, the limits of the axes may be similar to that of the article so that the shape can be seen in more detail in order to be able to compare better.

Also, I think there was a mistake in function G.

G := (t,x,y) -> mu*beta*x*y/(a+x^2) - d*y - eta*x*y;

@Rouben Rostamian Thanks but I n...

Answered: torabi 85

March 16 2018

0 0

@Rouben Rostamian

Thanks but I need a code for fractional Adams-Bashforth-Moulton method in maple as I said in first post.

Thabks

some details...

Answered: torabi 85

March 11 2018

0 0

@Rouben Rostamian

It is optional for F and G.

I attached manuscript for more details.

Thanks

115006_listening_sample_task_-_matching_example_1_.pdf

program code...

Answered: torabi 85

March 09 2018

0 0

how I can write above equation as a program code for fractional Adams-Bashforth-Moulton method in maple?

thanks

No numerical solution....

Answered: torabi 85

March 03 2018

0 0

@Kitonum

No numerical solution. I need a function that satisfies zero boundary conditions.

for example u(r)=.... same as you find in general condition that u(R0) = U2, u(h) = U1

but this time u(R0) = 0, u(h) = 0

if U1=U2=0 then the function will be zer...

Answered: torabi 85

March 02 2018

0 0

@Kitonum

Thanks for the reply.

if U1=U2=0 then the function will be zero!. Is there other option for selecting this function u(r)?

thanks

zero answer...

Answered: torabi 85

January 16 2018

0 0

@Rouben Rostamian

thank you

I reform my equations but i gain only zero answer!!

I want gain other answer.

may you help me.

thanks

dsolve2.mw

restart; nt := 1; nb := 1; R0 := .9149; n := 2; PDE1 := (diff(r*(diff(theta(r), r)), r))/r+nb*(diff(theta(r), r))*(diff(sigma(r), r))+nt*(diff(theta(r), r))^2 = 0

((diff(diff(theta(r), r), r))*r+diff(theta(r), r))/r+(diff(theta(r), r))*(diff(sigma(r), r))+(diff(theta(r), r))^2 = 0

(1)

(diff(sigma(r), r)+r*(diff(diff(sigma(r), r), r)))/r+((diff(diff(theta(r), r), r))*r+diff(theta(r), r))/r = 0

(2)

dsys5 := {PDE1, PDE2, sigma(R0) = 0, theta(R0) = 0, (D(theta))(0) = 0, ((D@@1)(sigma))(0) = 0}; res := dsolve(dsys5, 'maxmesh' = 900, numeric, method = bvp[middefer], output = array([.1]))

array( 1 .. 2, 1 .. 1, [( 2, 1 ) = (array( 1 .. 1, 1 .. 5, [( 1, 5 ) = (HFloat(0.0)), ( 1, 1 ) = (.1), ( 1, 4 ) = (HFloat(0.0)), ( 1, 3 ) = (HFloat(0.0)), ( 1, 2 ) = (HFloat(0.0)) ] )), ( 1, 1 ) = (array( 1 .. 5, [( 1 ) = (r), ( 2 ) = (sigma(r)), ( 3 ) = (diff(sigma(r), r)), ( 4 ) = (theta(r)), ( 5 ) = (diff(theta(r), r)) ] )) ] )

(3)

>

$proc (x_bvp) local res, data, solnproc, _ndsol, outpoint, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](x_bvp) else outpoint := evalf(x_bvp) end if; data := Array(1..4, {(1) = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; X := Vector(8, {(1) = .0, (2) = .13069999999999998, (3) = .26139999999999997, (4) = .3921, (5) = .5228, (6) = .6535000000000001, (7) = .7842000000000001, (8) = .9149}, datatype = float[8], order = C_order); Y := Matrix(8, 4, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = .0}, datatype = float[8], order = C_order); YP := Matrix(8, 4, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = -.0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = -.0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = -.0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = -.0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = -.0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = -.0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = -.0}, datatype = float[8], order = C_order); errproc := proc (x_bvp) local outpoint, X, Y, yout, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; Digits := 15; outpoint := evalf(x_bvp); X := Vector(8, {(1) = .0, (2) = .13069999999999998, (3) = .26139999999999997, (4) = .3921, (5) = .5228, (6) = .6535000000000001, (7) = .7842000000000001, (8) = .9149}, datatype = float[8], order = C_order); Y := Matrix(8, 4, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = .0}, datatype = float[8], order = C_order); if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "right" then return X[8] elif outpoint = "order" then return 2 elif outpoint = "error" then return 0. elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [4, 8, [sigma(r), diff(sigma(r), r), theta(r), diff(theta(r), r)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[8] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[8] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(4, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(8, 4, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(4, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(8, 4, X, Y, outpoint, yout, L, V) end if; [r = outpoint, seq('[sigma(r), diff(sigma(r), r), theta(r), diff(theta(r), r)]'[i] = yout[i], i = 1 .. 4)] end proc; if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "method" then return "bvp" elif outpoint = "right" then return X[8] elif outpoint = "order" then return 2 elif outpoint = "error" then return 0. elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [4, 8, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[8] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[8] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (true), ( 6 ) = (false) ] ); L := Matrix(7, 2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0, (3, 1) = .0, (3, 2) = .0, (4, 1) = .0, (4, 2) = .0, (5, 1) = .0, (5, 2) = .0, (6, 1) = .0, (6, 2) = .0, (7, 1) = .0, (7, 2) = .0}, datatype = float[8], order = C_order); yout := Vector(4, {(1) = .0, (2) = .0, (3) = .0, (4) = .0}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(8, 4, X, Y, YP, outpoint, var(yout), var(L), var(V))) else if _EnvInFsolve = true then Digits := _EnvDSNumericSaveDigits end if; V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (true), ( 6 ) = (false) ] ); L := Matrix(7, 2, {(1, 1) = 0., (1, 2) = 0., (2, 1) = 0., (2, 2) = 0., (3, 1) = 0., (3, 2) = 0., (4, 1) = 0., (4, 2) = 0., (5, 1) = 0., (5, 2) = 0., (6, 1) = 0., (6, 2) = 0., (7, 1) = 0., (7, 2) = 0.}, order = C_order); yout := Vector(4, {(1) = 0., (2) = 0., (3) = 0., (4) = 0.}); `dsolve/numeric/hermite`(8, 4, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 4)] end proc, (2) = Array(0..0, {}), (3) = [r, sigma(r), diff(sigma(r), r), theta(r), diff(theta(r), r)], (4) = 0}); solnproc := data[1]; if not type(outpoint, 'numeric') then if outpoint = "solnprocedure" then return eval(solnproc) elif member(outpoint, ["start", "left", "right", "errorproc", "rawdata", "order", "error"]) then return solnproc(x_bvp) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(x_bvp) else _ndsol := pointto(data[2][0]); return ('_ndsol')(x_bvp) end if end if; try res := solnproc(outpoint); [r = res[1], seq('[sigma(r), diff(sigma(r), r), theta(r), diff(theta(r), r)]'[i] = res[i+1], i = 1 .. 4)] catch: error end try end proc$