# Question:Error from pdsolve using periodic BC.

## Question:Error from pdsolve using periodic BC.

Maple 2019

Why Maple 2019.1 gives an error when no initial conditions are given for the following heat PDE with periodic BC?

I am using Physics 426 (current version). On windows 10.

When adding ic as some arbitrary function f(x), then the error goes away. But no ic needs to be given to solve this PDE. The answer can be left using arbitrary constants in this case.

I also found that this seems to happen when the BC are periodic. When using the normal Dirichlet B.C. and omitting the initial conditions, the error went away.

Am I doing something wrong or is this a bug?

 > restart;
 > pde:=diff(u(x,t),t)=diff(u(x,t),x\$2); #try with NO IC bc:=u(-Pi,t)=u(Pi,t),D[1](u)(-Pi,t)=D[1](u)(Pi,t); pdsolve([pde,bc],u(x,t))

Error, (in pdsolve/BC/2nd_order/Series/TwoBC) invalid boolean expression: NULL

 > restart;
 > pde:=diff(u(x,t),t)=diff(u(x,t),x\$2)-u(x,t); #now try with IC bc:=u(-Pi,t)=u(Pi,t),D[1](u)(-Pi,t)=D[1](u)(Pi,t); ic:=u(x,0)=f(x); pdsolve([pde,bc,ic],u(x,t)); #solution is correct
 >

 > restart;
 > pde:=diff(u(x,t),t)=diff(u(x,t),x\$2); #now try with NO IC, but not periodic BC bc:=u(0,t)=1,u(Pi,t)=0; pdsolve([pde,bc],u(x,t)); #solution is correct

 >