I am going to get the price of a zero coupon bond in a jump-diffusion model. The dynamic of interest rate as follow $$dr_t=\kappa(\theta-r_t)dt+\sigma\sqrt{r_t}\,dW_t+d\left(\sum\limits_{i=1}^{N_t}\,J_i\right)$$ where $N_t$ represents a Poisson process with constant intensity rate $\lambda>0$ and $\{J_i\}_{i=1}^{\infty}$ denotes the magnitudes of jump, which are assumed to be i.i.d. random variables with distribution $f_J$ independent of $W_t$ and $N_t$. Moreover,$W_t$ is assumed to be independent of $N_t$. In addition the jump sizes $\,J_i$ has an exponential distribution with density: $${{f}_{J}}(\chi )=\left\{ \begin{matrix} \eta {{e}^{-\eta\,\chi}}\,,\,\,\chi >0\, \\ 0\,\,\,\,\,\,\,\,,\,\,\,\,o.w. \\ \end{matrix} \right.$$ where $\eta > 0 $ is an constant. I can prove the arbitrage-free price at time $t$ of a traded interest rate security with paying $H(r)\in\,\mathcal{L^1}(\Omega\,,\,\mathcal{F}_T\,,\,Q)$ and maturity $T$ satisfies the following parabolic partial integro differential equation $$\frac{\partial F}{\partial t}+\frac{1}{2}{{\sigma }^{2}}r\frac{{{\partial }^{2}}F}{\partial {{r}^{2}}}+\kappa (\theta -r)\frac{\partial F}{\partial r}-rF+\lambda \int_{-\infty }^{\infty }{(F(t,r+\chi ,T)-F(t,r,T)d\chi =0}$$ with boundary condition $F(T,r,T)=H(r)$. Obviously in the case of zero-coupon bond we have $$H(r)=P(T,r,T)=1$$
My Challenge
I want to solve this PIDE leading to the bond pricing formula but I have no good idea. I know $$F(t,r,T)={{E}}^{\mathbb{Q}}\left[ {{e}^{-\int_{t}^{T}{{{r}_{s}}ds}}}|{\mathcal{F}_{t}} \right]=\exp \left[ A(T,t)-B(t,T){{r}_{t}} \right] \,\,\,\,\,\,(1)$$ but I can't extract these deterministic functions. Indeed, I substitute $(1)$ into PIDE. I then have a system of two ordinary differential equations that determine the coefficient functions.
How can I approximate this PIDE by Numerical Methods? Indeed, I have no other boundary conditions.