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mehdi jafari

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solve integro-differential equation...

mehdi jafari 749 Maple
ode dsolve numeric
November 19 2020
1 6

how this integro-differential equation can be solved?
any assumption or suggestion is appreciated. tnx in advance

EDITED: parameters are added.


 

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restart
> 

w[c]:=0.01:delta:=5:Omega:=5:w[0]:=1:gamma_0:=1:k[b]:=1:T:=100:nu[n]:=2*Pi*n*k[b]*T;

200*Pi*n

 (1)
> 

F:=2*gamma_0*w[c]^2*exp(-w[c]*tau)*sin(delta/Omega*(sin(Omega*t)-sin(Omega*(t-tau)))+w[0]*tau):
> 

k1:=2*k[b]*T*w[c]^2*sum((w[c]*exp(-w[c]*tau)-abs(nu[n])*exp(-abs(nu[n])*tau))/(w[c]^2-nu[n]^2),n=-infinity..infinity):
> 

G:=cos(delta/Omega*(sin(Omega*t)-sin(Omega*(t-tau)))+w[0]*tau)*k1:
> 

eq:=diff(rho(t),t)+Int(G*rho(tau),tau=0..t)=1/2*Int(G-F,tau=0..t);

diff(rho(t), t)+Int(0.200e-1*cos(sin(5*t)-sin(5*t-5*tau)+tau)*(sum((0.1000000000e-1*exp(-0.1000000000e-1*tau)-628.3185308*abs(n)*exp(-628.3185308*abs(n)*tau))/(-394784.1762*n^2+0.1000000000e-3), n = -infinity .. infinity))*rho(tau), tau = 0 .. t) = (1/2)*(Int(0.200e-1*cos(sin(5*t)-sin(5*t-5*tau)+tau)*(sum((0.1000000000e-1*exp(-0.1000000000e-1*tau)-628.3185308*abs(n)*exp(-628.3185308*abs(n)*tau))/(-394784.1762*n^2+0.1000000000e-3), n = -infinity .. infinity))-0.2e-3*exp(-0.1e-1*tau)*sin(sin(5*t)-sin(5*t-5*tau)+tau), tau = 0 .. t))

 (2)
> 

 


 

Download integro.mw

find an explicit function of two functio...

mehdi jafari 749 Maple
ode dsolve explicit
November 12 2020
2 6

i have ode system of two dependent variables y and x  and one independent varibale time. how can i find explicit expression between y and x? 

 

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restart
> 

sys:=diff(x(t),t)=x(t)*y(t)+t,diff(y(t),t)=x(t)-t;

diff(x(t), t) = x(t)*y(t)+t, diff(y(t), t) = x(t)-t

 (1)
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dsolve([sys,x(0)=0,y(0)=1],[x(t),y(t)],series)

{x(t) = series((1/2)*t^2+(1/6)*t^3+(1/24)*t^4-(1/24)*t^5+O(t^6),t,6), y(t) = series(1-(1/2)*t^2+(1/6)*t^3+(1/24)*t^4+(1/120)*t^5+O(t^6),t,6)}

 (2)
> 

 

> 

 

> 

 


 

Download explicit.mw

an ode problem with different results in...

mehdi jafari 749 Maple
October 09 2020
1 3

I have a system of six ODEs. i solve them numerically using dolve,numeric command. the problem is setting step size for example stepsize=1e-5 or minstep=500 lead to a result of order 1e-2; But without using this option, results are of order integer numbers. could any one help? tnx in advance

EDITED
 

Download ode_problem.mw

solve a nonlinear inequality...

mehdi jafari 749 Maple
solve inequality
July 23 2020
1 1

i have a nonlinear inequality which is plotted using plots:-inequl
can i find an algebric solution for this inequality? for example sth like this : 0.08<t<10 
thnx in advance

 

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restart:with(plots):with(Optimization):
> 

with(SolveTools[Inequality]):
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k := 1; c := 5; sigma := .85;N=10;

1

  

5

  

.85

  

N = 10

 (1)
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x:=t->4*exp(-t);

proc (t) options operator, arrow; 4*exp(-t) end proc

 (2)
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t0:=0.0065:
> 

inequal(sigma*k/(2*c+k)*abs(x(t))<abs(x(t)-x(t0)),t=0..10,x=0..4)

 
> 

 

> 

 

NULL


 

Download inequality.mw

define a system of Recurrence relations...

mehdi jafari 749 Maple
recurrence plotting
March 31 2020
2 5

How these system of relations can be defined and plotted?(with any possible assumptions)

 

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restart
> 

x[n+1]=1/3*(2*x[n]*y[n]+4*x[n]*z[n])+1/12*(2*x[n-1]*y[n-1]+4*x[n-1]*z[n-1])

x[n+1] = (2/3)*x[n]*y[n]+(4/3)*x[n]*z[n]+(1/6)*x[n-1]*y[n-1]+(1/3)*x[n-1]*z[n-1]

 (1)
> 

y[n+1]=1/3*(1/4*x[n]*z[n]+y[n])+1/12*(1/4*x[n-1]*z[n-1]+y[n-1])

y[n+1] = (1/12)*x[n]*z[n]+(1/3)*y[n]+(1/48)*x[n-1]*z[n-1]+(1/12)*y[n-1]

 (2)
> 

z[n+1]=1/3*(x[n]*z[n]+2*y[n]*z[n])+1/12*(x[n-1]*z[n-1]+2*y[n-1]*z[n-1])

z[n+1] = (1/3)*x[n]*z[n]+(2/3)*y[n]*z[n]+(1/12)*x[n-1]*z[n-1]+(1/6)*y[n-1]*z[n-1]

 (3)
> 

 


 

Download problem.mw

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