For implicit solvers such as ode23t, Simulink must compute the solver Jacobian, which is a submatrix of the Jacobian matrix associated with the continuous representation of a Simulink model.
In the full perturbation method Simulink solves the full set of perturbation equations and uses LAPACK for linear algebraic operations. This method is costly from a computational standpoint, but it remains the recommended method for establishing baseline results. The sparse perturbation method attempts to improve the run-time performance by taking mathematical advantage of the sparse Jacobian pattern.
The Sparse Perturbation Method and the Sparse Analytical Method may be able to take advantage of the sparsity pattern of the matrix to reduce the number of computations necessary and improve performance.
After running the profiler for all of these, Sparse pertubration method will give you the best performance. For more details refer the documentation link on choosing the solver:
If it supports your workflow, you can also try increasing the maximum step size of the solver as suggested in the screenshot you attached.
