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Question: solve a system of integral equations

Question:solve a system of integral equations

mehdi jafari 769 Maple
integration fsolve numeric
January 31 2020
1

how i can solve a system of integral equations? thanks for the help.
 

restart; with(LinearAlgebra); with(VectorCalculus)

pin1 := 1858.; pout1 := 0; pin2 := 0.1858e5; pout2 := 0; S := 1; T := 10; Fa1 := 0.; Fa2 := 0.
``

T[rr] := -pin-C10*simplify(int(B^2*sqrt((r^2-A)/B)^(2+m)/r^3-r/sqrt((r^2-A)/B)^(2-m), r = s .. t))/S^m-C20*simplify(int(r/(B^2*sqrt((r^2-A)/B)^(2-n))-sqrt((r^2-A)/B)^(2+n)/r^3, r = s .. t))/S^n

eq1 := C10*simplify(int((-2*A*r^2+A^2)/(r^3*sqrt((r^2-A)/B)^(2-m)), r = s .. t))/S^m+C20*simplify(int((2*A*r^2-A^2)/(B^2*r^3*sqrt((r^2-A)/B)^(2-n)), r = s .. t))/S^n

eq2 := 2*Pi*simplify(int(T[rr]*r, r = s .. t))-2*Pi*C10*simplify(int((B^4*sqrt((r^2-A)/B)^(2+m)-r^2*sqrt((r^2-A)/B)^m)/(B^2*r), r = s .. t))/S^m-2*Pi*C20*simplify(int((-B^3*r^3+A*B^3*r+r^3)/(B^2*sqrt((r^2-A)/B)^(2-n)), r = s .. t))/S^n

A := 0.50456255261718905958813087648305534133592085046840e-2; B := 1.0000045465297826882965065372650452712135679772907; S := 1; T := 10; Eq1 := simplify(subs([t = sqrt(B*T^2+A), s = sqrt(B*S^2+A)], eq1)); Eq2 := simplify(subs([pin = 1858., t = sqrt(B*T^2+A), s = sqrt(B*S^2+A)], eq2))

6.283156738*(int(0.5045671411e-2*C10*r*(int((2.*r^2-0.5045625526e-2)*(.9999954530*r^2-0.5045602584e-2)^((1/2)*m)/(r^3*(r^2-0.5045625526e-2)), r = 1.002521906 .. 10.00027501))-0.5045625526e-2*C20*r*(int((2.*r^2-0.5045625526e-2)*(.9999954530*r^2-0.5045602584e-2)^((1/2)*n)/((r^2-0.5045625526e-2)*r^3), r = 1.002521906 .. 10.00027501))-1858.008448*r, r = 1.002521906 .. 10.00027501))-6.283128170*C10*(int((.9999954530*r^2-0.5045602584e-2)^((1/2)*m)*(0.13641e-4*r^2-0.5045694353e-2)/r, r = 1.002521906 .. 10.00027501))+6.283156738*C20*(int((0.1364100000e-4*r^3-0.5045694353e-2*r)*(.9999954530*r^2-0.5045602584e-2)^((1/2)*n)/(r^2-0.5045625526e-2), r = 1.002521906 .. 10.00027501))

 (1)

``

Eq3 := simplify(subs([t = sqrt(B*T^2+A), s = sqrt(B*S^2+A)], eq1)); Eq4 := simplify(subs([pin = 0.1858e5, t = sqrt(B*T^2+A), s = sqrt(B*S^2+A)], eq2))

6.283156738*(int(0.5045671411e-2*C10*r*(int((2.*r^2-0.5045625526e-2)*(.9999954530*r^2-0.5045602584e-2)^((1/2)*m)/(r^3*(r^2-0.5045625526e-2)), r = 1.002521906 .. 10.00027501))-0.5045625526e-2*C20*r*(int((2.*r^2-0.5045625526e-2)*(.9999954530*r^2-0.5045602584e-2)^((1/2)*n)/((r^2-0.5045625526e-2)*r^3), r = 1.002521906 .. 10.00027501))-18580.08448*r, r = 1.002521906 .. 10.00027501))-6.283128170*C10*(int((.9999954530*r^2-0.5045602584e-2)^((1/2)*m)*(0.13641e-4*r^2-0.5045694353e-2)/r, r = 1.002521906 .. 10.00027501))+6.283156738*C20*(int((0.1364100000e-4*r^3-0.5045694353e-2*r)*(.9999954530*r^2-0.5045602584e-2)^((1/2)*n)/(r^2-0.5045625526e-2), r = 1.002521906 .. 10.00027501))

 (2)

  ``

NULL

ANS := fsolve({Eq1 = pout1-pin1, Eq2 = Fa1, Eq3 = pout2-pin2, Eq4 = Fa2}, {C10, C20, m, n})

``

NULL

NULL


 

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