If IC/BCs are approximated within, say 2% error, how much will the solution to the PDE solved using the Laplace transform deviate from the actual solution (solved with exact BC/ICs). Specifically, I'm currently solving the following PDE: $$\frac{D}{r^2}\frac{\partial}{\partial r}(r^2\frac{\partial C}{\partial r}) = \frac{\partial C}{\partial t}, r>b, t>0$$ $$\Gamma(t=0)=0$$ $$C(r>b,t=0)=C_0$$ $$C(r \to \infty,t>0)=C_0$$ $$\frac{\partial \Gamma}{\partial t}=D\frac{\partial}{\partial r}C( r=b, t>0)$$ $$\frac{\partial \Gamma}{\partial t}= \beta C(r=b,t>0)(1-\frac{\Gamma}{\Gamma_\infty})-\alpha e^{\phi(\Gamma)} \Gamma$$
And I want to know whether the solution to this PDE will still be accurate (under 2% error) if the last boundary condition is estimated by $$\frac{\partial \Gamma}{\partial t}= \beta C(r=b,t>0)$$ instead, which is known to deviate from the from the actual BC by an error of less than 2%.