Hello, I am trying to solve a system of partial differential equations that also contains a time delay part. For DDE, people usually use “DDEProblem” and for PDE people use “ODEProblem”. But, when I am trying to solve my two PDE coupled equations by using finite-differences scheme, then I am facing problmes. If I am using DDEProblem to solve it, then solution is become unstable. If I am trying to use ODEProblem, then it is not allowing me to use h(p,t) history function and error is coming that it is not compatible with ODEProblem. What should I do?

PDE people use whatever the discretization gives. For your case, it should give a DDEProblem.

What’s your discretization like? Is it a stable discretization? Are you using an implicit method? Etc. There’s little information here.