A new class of algorithms for solving nonlinear structural dynamical problems are derived in the present paper, as being based on optimal-feedback-accelerated Picard iteration, wherein the solution vectors for the displacements and velocities at any time in a finitely large time interval are corrected by a weighted (with a matrix) integral of the error. We present 3 approximations to solve the Euler-Lagrange equations for the optimal weighting functions; thus we present 3 algorithms denoted as Optimal-Feedback-Accelerated Picard Iteration (OFAPI) algorithms-1, 2, 3.
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