mehdi jafari

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6 years, 345 days

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These are questions asked by mehdi jafari

i have a problem with a nonlinear equation containing Heaviside step function. fsolve does not return anything and SolveEquation command also returns incorrect answer. How can i solve this equation? any method or help is appreciated.


 

 

restart:

with(DirectSearch):

F:=x*(Heaviside(x-(S0))/(1-DD)+Heaviside(-x+S0)/(1-HH*DD));

x*(Heaviside(x-S0)/(1-DD)+Heaviside(-x+S0)/(-DD*HH+1))

(1)

EQ:=F-E*Y;

-E*Y+x*(Heaviside(x-S0)/(1-DD)+Heaviside(-x+S0)/(-DD*HH+1))

(2)

HH:=0.2;
DD:=0.579350262599427;
S0:=1e8;
E:=70e9;
Y:=0.001668993263529;

.2

 

.579350262599427

 

0.1e9

 

0.70e11

 

0.1668993263529e-2

(3)

EQ

-116829528.5+x*(2.377274752*Heaviside(x-0.1e9)+1.131055455*Heaviside(-x+0.1e9))

(4)

fsolve(EQ)

fsolve(-116829528.5+x*(2.377274752*Heaviside(x-0.1e9)+1.131055455*Heaviside(-x+0.1e9)), x)

(5)

SolveEquations(EQ)

Warning, complex or non-numeric value encountered; trying to find a feasible point

 

[1.3868049384289111*10^13, Vector(1, {(1) = -3723983.000}), [x = 9.999999999999999*10^7], 231]

(6)

eval(EQ,x = 1.00000000000000*10^8)

Float(undefined)

(7)

 


 

Download fsolve.mw

i have two expressions. S1 and S2 are functions of sigma and tau. but i need derivative of sigma and tau with respect to S1 and S2. what should i do ? could any one help?


 

restart

S1 := -4*sqrt(sigma1^2 + 4*tau^2)*tau^2/((sigma1 + sqrt(sigma1^2 + 4*tau^2))^2*(1 + 4*abs(tau/(sigma1 + sqrt(sigma1^2 + 4*tau^2)))^2))

-4*(sigma1^2+4*tau^2)^(1/2)*tau^2/((sigma1+(sigma1^2+4*tau^2)^(1/2))^2*(1+4*abs(tau/(sigma1+(sigma1^2+4*tau^2)^(1/2)))^2))

(1)

S2 := 4*sqrt(sigma1^2 + 4*tau^2)*tau^2/((-sigma1 + sqrt(sigma1^2 + 4*tau^2))^2*(1 + 4*abs(tau/(-sigma1 + sqrt(sigma1^2 + 4*tau^2)))^2))

4*(sigma1^2+4*tau^2)^(1/2)*tau^2/((-sigma1+(sigma1^2+4*tau^2)^(1/2))^2*(1+4*abs(tau/(-sigma1+(sigma1^2+4*tau^2)^(1/2)))^2))

(2)

 

 

 


 

Download chain_rule_derivative.mw

Hi. how can maple determine whether a vector is linear compostion of two or more vectors? 
for example w=a*v+b*u so that w is linear compostion of vectors u and v ( a and b are scalar numbers). tnx for the help.

i have two ode equations, when try to solve, i face this error
Error, (in dsolve/numeric/bvp/convertsys) unable to convert to an explicit first-order system
any comment or help to solve this? ( or any simplifying comments to solve) . thnx in advance

 

restart

A := 4263736263.736263:B := 11868131.86813187:C := 600146.5201465202:hr := 0.3e7:muz := 0.2632654643708247e-5:P:=1000:

1000

(1)

ode1 := diff(u(r), r, r)+(diff(u(r), r))/r-u(r)/r^2-B*(diff(w(r), r, r, r)+(diff(w(r), r, r))/r-(diff(w(r), r))/r^2)/A = 0;

diff(diff(u(r), r), r)+(diff(u(r), r))/r-u(r)/r^2-0.2783505155e-2*(diff(diff(diff(w(r), r), r), r))-0.2783505155e-2*(diff(diff(w(r), r), r))/r+0.2783505155e-2*(diff(w(r), r))/r^2 = 0

(2)

ode2 := C*(diff(w(r), r, r, r, r))+2*C*(diff(w(r), r, r, r))/r-(C/r^2+muz*hr^2)*(diff(w(r), r, r))+(C/r^3-muz*hr^2/r)*(diff(w(r), r))+muz*hr^2*w(r)/r^2-B*(diff(u(r), r, r, r))-2*B*(diff(u(r), r, r))/r+B*(diff(u(r), r))/r^2-B*u(r)/r^3 = P;

600146.5201465202*(diff(diff(diff(diff(w(r), r), r), r), r))+1200293.040*(diff(diff(diff(w(r), r), r), r))/r-(600146.5201465202/r^2+23693891.80)*(diff(diff(w(r), r), r))+(600146.5201465202/r^3-23693891.80/r)*(diff(w(r), r))+23693891.80*w(r)/r^2-11868131.86813187*(diff(diff(diff(u(r), r), r), r))-23736263.74*(diff(diff(u(r), r), r))/r+11868131.86813187*(diff(u(r), r))/r^2-11868131.86813187*u(r)/r^3 = 1000

(3)

ics := w(.2) = 0, (D(w))(.2) = 0, w(1) = 0, (D(w))(1) = 0, u(.2) = 0, u(1) = 0;

w(.2) = 0, (D(w))(.2) = 0, w(1) = 0, (D(w))(1) = 0, u(.2) = 0, u(1) = 0

(4)

dsolve({ode1,ode2} union {ics},{w(r),u(r)},numeric)

Error, (in dsolve/numeric/bvp/convertsys) unable to convert to an explicit first-order system

 

 

 

Download zzv.mw

i want to solve an integration as a funstion of T, but it return the integral unevaluated, but when i change the place of "numeric option" it returns sth. what is the problem ?
 

restart:with(RealDomain):

simplify((2/pi)^(1/2)*(int((exp(-32.74123792568-0.8916456579806e-1*ln(4.852623952*10^9*v^2)))*exp(-v^2/(2*T))*v^3, v = 2 .. 100,numeric,AllSolutions)))

2^(1/2)*(1/pi)^(1/2)*(int(exp((-34.72985611*T-.1783291316*ln(v)*T-.5*v^2)/T)*v^3, v = 2 .. 100, AllSolutions))

(1)

simplify((2/pi)^(1/2)*(int((exp(-32.74123792568-0.8916456579806e-1*ln(4.852623952*10^9*v^2)), numeric)*exp(-v^2/(2*T))*v^3, v = 2 .. 100)), AllSolutions);

.2419366578*exp((-32.74123793*T-5000.000000)/T)*((1.000000000*T+2.000000001)*exp(4998./T)-.5022352314*exp(5000./T)*T-.4977647690*T-2488.823845)*(1/pi)^(1/2)*2^(1/2)*T

(2)

 

NULL


 

Download int.mw

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