We investigated numerical methods for predictors in a multiscale cardiovascular simulation model. The proposed method predicts initial approximations for the iterative convergence calculations of the strong coupling method using the smoothing spline to remove errors from values of past timesteps and using the linear and second-order extrapolation. The new coupling algorithm was used for coupling a left ventricular finite element model to a myocardial excitation-contraction model. We performed experiments with different values for the smoothing parameter λ and with linear and second-order extrapolations. λ = 1 with the linear extrapolation gave the best results. It reduced computation time by 91% compared to the strong coupling method. With the use of the smoothing spline, distance between the initial approximation and converged solution reduced by 62%, while the average number of iterations reduced by 32%. The smoothing spline can be used to improve the accuracy of predictors and reduce the number of iterations needed for the computation of the convergence procedure.