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We study the massive ODE/IM correspondence for modified $B_2^{(1)}$ affineToda field equation. Based on the $\psi$-system for the solutions of theassociated linear problem, we obtain the Bethe ansatz equations. We alsodiscuss the T-Q relations, the T-system and the Y-system, which are shown to berelated to those of the $A_3/{\bf Z}_2$ integrable system. We consider the casethat the solution of the linear problem has a monodromy around the origin,which imposes nontrivial boundary conditions for the T-/Y-system. Thehigh-temperature limit of the T- and Y-system and their monodromy dependenceare studied numerically.

ODE/IM correspondence for modified $B_2^{(1)}$ affine Toda field equation