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Question: numerical error around point -1

Question:numerical error around point -1

NIMA112 50 Maple 2020
integration contour plotting
September 14 2023
0

hello,

I computed some algebraic calculation, but near point -1 there is some issue like disconvergencies. Can anyone help in this regard? In the final graph, as seen the paths of the curves are close together and convergence does not occur AROUND POINT -1.

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restart
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Digite := 30

30

 (1)
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beta := 2.5; lambda := 0.1e-1; b := Pi; a := Pi; alpha := 0; y[1] := 1.5; y[2] := 1.5; x[1] := -1; x[2] := 1; Q[1] := 40; Q[2] := 35; T[1] := 20

2.5

  

0.1e-1

  

Pi

  

Pi

  

0

  

1.5

  

1.5

  

-1

  

1

  

40

  

35

 (2)
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v := (2*n-1)*Pi/(2*b)
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Delta := exp(2*v*a)*(alpha*v+beta)*(1+lambda)-(1-lambda)*(alpha*v-beta)
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omega := Pi/(2*b)
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P[1] := ((1+lambda)*exp(-v*abs(x-xi))+(1-lambda)*exp(v*(x+xi)))*exp(2*v*a)+(1+lambda)*exp(-v*(x+xi))+(1-lambda)*exp(v*abs(x-xi))
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P[2] := ((1+lambda)*exp(-v*abs(x-xi))+(1-lambda)*exp(v*(x+xi)))*exp(2*v*a)-(1+lambda)*exp(-v*(x+xi))-(1-lambda)*exp(v*abs(x-xi))
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P[3] := P[1]*(-alpha^2*v-alpha*beta+alpha*v)+beta*P[2]
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G[11] := (sum((alpha*P[1]*(1-lambda)*(alpha*v-beta)*exp(-2*v*a)+(1+lambda)*P[3])*(cos(v*(y-eta))-cos(v*(y+eta)))/(v*(exp(2*v*a)*(alpha*v+beta)*(1+lambda)-(1-lambda)*(alpha*v-beta))), n = 1 .. 80))/(2*b*(1+lambda))+(2*(1+lambda)*alpha*b/Pi*.25)*ln((1+2*exp(-omega*abs(x-xi))*cos(omega*(y-eta))+exp(-2*omega*abs(x-xi)))*(1-2*exp(-omega*abs(x-xi))*cos(omega*(y+eta))+exp(-2*omega*abs(x-xi)))*(1+2*exp(-omega*(2*a+x+xi))*cos(omega*(y-eta))+exp(-2*omega*(2*a+x+xi)))*(1-2*exp(-omega*(2*a+x+xi))*cos(omega*(y+eta))+exp(-2*omega*(2*a+x+xi)))/((1-2*exp(-omega*abs(x-xi))*cos(omega*(y-eta))+exp(-2*omega*abs(x-xi)))*(1+2*exp(-omega*abs(x-xi))*cos(omega*(y+eta))+exp(-2*omega*abs(x-xi)))*(1-2*exp(-omega*(2*a+x+xi))*cos(omega*(y-eta))+exp(-2*omega*(2*a+x+xi)))*(1+2*exp(-omega*(2*a+x+xi))*cos(omega*(y+eta))+exp(-2*omega*(2*a+x+xi)))))/(2*b*(1+lambda))+(2*(1-lambda)*alpha*b/Pi*.25)*ln((1+2*exp(omega*(x+xi))*cos(omega*(y-eta))+exp(2*omega*(x+xi)))*(1-2*exp(omega*(x+xi))*cos(omega*(y+eta))+exp(2*omega*(x+xi)))*(1+2*exp(-omega*(2*a-abs(x-xi)))*cos(omega*(y-eta))+exp(-2*omega*(2*a-abs(x-xi))))*(1-2*exp(-omega*(2*a-abs(x-xi)))*cos(omega*(y+eta))+exp(-2*omega*(2*a-abs(x-xi))))/((1-2*exp(omega*(x+xi))*cos(omega*(y-eta))+exp(2*omega*(x+xi)))*(1+2*exp(omega*(x+xi))*cos(omega*(y+eta))+exp(2*omega*(x+xi)))*(1-2*exp(-omega*(2*a-abs(x-xi)))*cos(omega*(y-eta))+exp(-2*omega*(2*a-abs(x-xi))))*(1+2*exp(-omega*(2*a-abs(x-xi)))*cos(omega*(y+eta))+exp(-2*omega*(2*a-abs(x-xi))))))/(2*b*(1+lambda))
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g[12] := lambda*((alpha*v+beta)*exp(v*(2*a+x))+(alpha*v-beta)*exp(-v*x))*exp(-v*xi)/(v*Delta)
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G[12] := (sum(g[12]*(cos(v*(y-eta))-cos(v*(y+eta))), n = 1 .. 80))/b
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phi[1] := int(int(G[11]*Q[1]*Dirac(xi-x[1])*Dirac(eta-y[1]), xi = -a .. 0), eta = 0 .. b)+int(int(G[12]*Q[2]*Dirac(xi-x[2])*Dirac(eta-y[2]), xi = 0 .. infinity), eta = 0 .. b)
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Z[1] := diff(phi[1], x)
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psi[1] := int(Z[1], y)
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plot3d(psi[1], x = -a .. 0, y = 0 .. b)

 
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with(plots)
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contourplot(psi[1], x = -a .. 0, y = 0 .. b)

 
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