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How to find the n-th component?...

hind 45 Maple
December 22 2015
0 1

 

Qu_in_maple.mw

How to compute the  n component of U[i] even to reach the exact solution?

 

``

> 

k := proc (t) options operator, arrow; t end proc:
> 

U[0] := f(x):
> 

for i to N do U1[i-1] := subs(x = t, U[i-1]); U[i] := (1/2)*x^2*(int(t*U1[i-1], t = a .. b)) end do:
> 

Parse:-ConvertTo1D, "first argument to _Inert_ASSIGN must be assignable"

cos(x)+x^2+(1/2)*x^2*(-2+(1/4)*Pi^4)+(1/8)*x^2*(-1+(1/8)*Pi^4)*Pi^4+(1/64)*x^2*(-1+(1/8)*Pi^4)*Pi^8

  

cos(x)+(1/512)*x^2*Pi^12

 (1)
> 

Exact := proc (x) options operator, arrow; cos(x) end proc

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Download Qu_in_maple.mwQu_in_maple.mw

How to find the  n component of U[i] even to reach the Exact solution cos(x)

Why doesn't it work correctly?...

hind 45 Maple
recurrence
December 20 2015
1 0

 

How to  compute the recurrence relation and I find the problem when the summation of U because appear noise term self-canceling and I can not find the nth component of U?Mixed_volterra_-Fredholm_(278)_Ex(8.17).mw

"this program is solving Mixed Fredholmvolterra integral equation using modified decomposition method page 278 Example(8.17) by Creation date : (9\3\1437) ------------------------------ u(x)=f(x,t)+(∫)[0]^(t)(∫)[0]^(1)F(x,t,r,s)*u(r,s) ⅆr ds. -----------------------------"

> 

restart
> 

f := proc (x, t) options operator, arrow; exp(-t)*(cos(x)+t*cos(x)+(1/2)*t*cos(x-1)*sin(1)) end proc:
> 

U[0] := f1(x, t):
> 

for i from 2 to 5 do U1[i-1] := subs({r = x, s = t}, U[i-1]); U[i] := simplify(-(int(int(F(x, t, r, s)*U1[i-1], r = 0 .. 1), s = 0 .. t))) end do:
> 

``

``

 

Download Mixed_volterra_-Fredholm_(278)_Ex(8.17).mwMixed_volterra_-Fredholm_(278)_Ex(8.17).mw

 

thank you for helping:)

How to evaluate the Abel integral?...

hind 45
integral abel operator
December 20 2015
1 3

How to evaluate The Abel integral has the form I can not compute this

> restart;

> f := proc (x) options operator, arrow; (4/3)*x^(3/2) end proc; k := proc (x, t) options operator, arrow; 1/sqrt(x-t) end proc;

> int((4/3)*t^(3/2)/sqrt(x-t), t = 0 .. x);

Thank you :)

 

> restart;> f := proc (x) options operator, arrow; (4/3)*x^(3/2) end proc; k := proc (x, t) options operator, arrow; 1/sqrt(x-t) end proc;> int((4/3)*t^(3/2)/sqrt(x-t), t = 0 .. x);

 

Integrate both sides...

hind 45 Maple
integro-differential-equation
November 12 2015
2 8

I want convert the integro differential equation to volterra integral equation by integration both side of integro-diff then subs in  initial condition 

intE := diff(u(x), x) = 1+x-x^2+int((x-t)*u(t), t = 0 .. x), u(0) = 3

How do it?

How to equate coefficients?...

hind 45 Maple
equate
November 12 2015
1 1

How equating the coefficient in the same power of x  

diff(u(x), x) = 1+int(u(t), t = 0 .. x), u(0) = 0

intE1 := subs({u(t) = sum(a[i]*t^i, i = 0 .. 3), u(x) = sum(a[i]*x^i, i = 0 .. 3)}, intE);
intE2 := eval(intE1);
intE3 := collect(intE2, x);
ans := zip(`=`, [coeffs(lhs(intE3)-rhs(intE3), [x, x^2, x^3, x^4], 't')], [seq(0, i = 1 .. nops([t]))]);

Shows me wrong I also want to find values of a[1] and a[2] and a[3] and a[4] without using my hand and from the initial condition a[0]=0?

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