kill(all)$

maxima:appendix:fvm:how to solve : inequalities,two methods,version 1.0
peter.vlasschaert@gmail.com,29/11/2022

see website 
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ref 1:
new:29/11/2022:maxima : heat conduction (unsteady),explicit,cank-nicolson,implicit no source (limit : Δt)

pratical 
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1e)  step :load packages
2e)  step :assume doesn't work for the packages
3e) step : inequalities must be list format
4e) step : variables to solve also list format.

load(to_poly_solve)$ -> %solv([inequalities],[Δt])
load(fourier_elim)$   →:fourier_elim([inequalities],[Δt])

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load(to_poly_solve)$

%solve([7*x+2<-x-3+Δx], [x]);

see : ref 1

q:(c·Δx·ρ)/Δt>(2·k)/Δx;

v1:%solve([(c·Δx·ρ)/Δt>(2·k)/Δx,k>0,Δx>0,c>0,ρ>0,c>0,Δt>0], [Δt]);

v1a:part(v1,1);

v1b:last(v1a);

v1ba:lhs(v1b)=0;

v1bb:v1ba-c*Δx^2*ρ;

v1bc:v1bb/(-2*k);

change :direction inequality,divide trough negativ value

→ correction : negative sign:((-)*2*k)

v1bd:lhs(v1bc)<rhs(v1bc);

load(fourier_elim)$

W1:fourier_elim([(c·Δx·ρ)/Δt>(2·k)/Δx,k>0,Δx>0,c>0,ρ>0,c>0,Δt>0], [Δt]);

rem : analog result of when use : load(to_poly_solve)

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