kill(all)$

appendix : maxima : fvm :steady equation for (convection(=lhs),diffusion(=rhs)),version 1.0 
peter.vlasschaert@gmail.com,21/10/2022

see website :
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new:20/10/2022:maxima :  fvm: code d(c)integrate(expr,var,lo,hi),version 1.0
download  (maxima,code)        :maximafvmdintegrateverison12022

fvm:finite volume method.

convection - diffusion equation 
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s1:'diff(u(x)*ρ(x)*Φ(x),x) = 'diff(Γ(x)*diff(Φ(x),x),x);

integration expr contains : differential  , between : aa1 ≤ xx1 ≤ bb1:
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dintegrate(pp1,xx1,aa1,bb1):=block([s1],
s1:integrate(pp1,xx1),
s2:at(s1,xx1=bb1)-at(s1,xx1=aa1),
return(s2)    
)$

s1a:dintegrate(lhs(s1),x,a,b) =dintegrate(rhs(s1),x,a,b);

idependent integration  :
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s2:integrate(s1,x);

rem : %c1 isn't function of x = constant
rem : integrate both sides (lhs & rhs)

flux = convection flux + diffusion flux.
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x-direction ( cartesian coordinates)

s3:Jx=lhs(s2) - part(rhs(s2),1);

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