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Question: pdetest Not Giving 0 for pdsolve

Question:pdetest Not Giving 0 for pdsolve

Test007 50 Maple 2020
pde pdsolve differential-equations pdetest
July 26 2020
0

Does anyone know why pdetest is not giving [0, 0, 0] for the solution of pdsolve?
 

> 

restart
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eq := diff(u(x, t), t)-k*(diff(u(x, t), x, x)) = 0

diff(u(x, t), t)-k*(diff(diff(u(x, t), x), x)) = 0

 (1)
> 

ic := u(x, 0) = g(x)

u(x, 0) = g(x)

 (2)
> 

bc := (D[1](u))(0, t) = 0, eval(diff(u(x, t), x)+u(x, t), x = 1) = 0

(D[1](u))(0, t) = 0, eval(diff(u(x, t), x), {x = 1})+u(1, t) = 0

 (3)
> 

sol := `assuming`([simplify(pdsolve([eq, ic, bc]))], [k > 0, 0 < x and x < 1, t > 0])

u(x, t) = `casesplit/ans`(Sum(4*exp(-k*lambda[n]^2*t)*lambda[n]*cos(lambda[n]*x)*(Int(g(x)*cos(lambda[n]*x), x = 0 .. 1))/(2*lambda[n]+sin(2*lambda[n])), n = 0 .. infinity), {And((sin(lambda[n])*lambda[n]-cos(lambda[n]))/cos(lambda[n]) = 0, 0 < lambda[n])})

 (4)
> 

`assuming`([simplify(pdetest(sol, [eq, ic, bc]))], [k > 0, 0 < x and x < 1, t > 0])

[-(diff(diff(`casesplit/ans`(sum(4*exp(-k*lambda[n]^2*t)*lambda[n]*cos(lambda[n]*x)*(Int(g(x)*cos(lambda[n]*x), x = 0 .. 1))/(2*lambda[n]+sin(2*lambda[n])), n = 0 .. infinity), {And(-(1/2)*(I*lambda[n]*exp(I*lambda[n])-I*lambda[n]*exp(-I*lambda[n])+exp(I*lambda[n])+exp(-I*lambda[n]))/cos(lambda[n]) = 0, 0 < lambda[n])}), x), x))*k+diff(`casesplit/ans`(sum(4*exp(-k*lambda[n]^2*t)*lambda[n]*cos(lambda[n]*x)*(Int(g(x)*cos(lambda[n]*x), x = 0 .. 1))/(2*lambda[n]+sin(2*lambda[n])), n = 0 .. infinity), {And(-(1/2)*(I*lambda[n]*exp(I*lambda[n])-I*lambda[n]*exp(-I*lambda[n])+exp(I*lambda[n])+exp(-I*lambda[n]))/cos(lambda[n]) = 0, 0 < lambda[n])}), t), `casesplit/ans`(Sum(4*lambda[n]*cos(lambda[n]*x)*(Int(g(x)*cos(lambda[n]*x), x = 0 .. 1))/(2*lambda[n]+sin(2*lambda[n])), n = 0 .. infinity), {And(-(1/2)*(I*lambda[n]*exp(I*lambda[n])-I*lambda[n]*exp(-I*lambda[n])+exp(I*lambda[n])+exp(-I*lambda[n]))/cos(lambda[n]) = 0, 0 < lambda[n])})-g(x), eval(diff(`casesplit/ans`(Sum(4*exp(-k*lambda[n]^2*t)*lambda[n]*cos(lambda[n]*x)*(Int(g(x)*cos(lambda[n]*x), x = 0 .. 1))/(2*lambda[n]+sin(2*lambda[n])), n = 0 .. infinity), {And(-(1/2)*(I*lambda[n]*exp(I*lambda[n])-I*lambda[n]*exp(-I*lambda[n])+exp(I*lambda[n])+exp(-I*lambda[n]))/cos(lambda[n]) = 0, 0 < lambda[n])}), x), {x = 0}), eval(diff(`casesplit/ans`(Sum(4*exp(-k*lambda[n]^2*t)*lambda[n]*cos(lambda[n]*x)*(Int(g(x)*cos(lambda[n]*x), x = 0 .. 1))/(2*lambda[n]+sin(2*lambda[n])), n = 0 .. infinity), {And(-(1/2)*(I*lambda[n]*exp(I*lambda[n])-I*lambda[n]*exp(-I*lambda[n])+exp(I*lambda[n])+exp(-I*lambda[n]))/cos(lambda[n]) = 0, 0 < lambda[n])}), x), {x = 1})+`casesplit/ans`(Sum(4*exp(-k*lambda[n]^2*t)*lambda[n]*cos(lambda[n])*(Int(g(x)*cos(lambda[n]*x), x = 0 .. 1))/(2*lambda[n]+sin(2*lambda[n])), n = 0 .. infinity), {And(-(1/2)*(I*lambda[n]*exp(I*lambda[n])-I*lambda[n]*exp(-I*lambda[n])+exp(I*lambda[n])+exp(-I*lambda[n]))/cos(lambda[n]) = 0, 0 < lambda[n])})]

 (5)
> 

``


 

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