The invention discloses a single
diagonal implicit Runge-Kutta method for simulating a second-order
differential equation, and the method comprises the steps: obtaining a simulated second-order
differential equation, converting the simulated second-order
differential equation into a target nonlinear equation, calculating a Jacobian matrix, constructing an iteration matrix, and carrying out the
decomposition of the Jacobian matrix; predicting the solution of the next
time step of the target nonlinear equation by using the explicit part of the single
diagonal implicit Runge-Kutta; the prediction result is used as an initial value of Newton iteration, a single
diagonal implicit Runge-Kutta method is adopted in the
iteration process, the prediction result is corrected to solve a target nonlinear equation, and iteration steps are repeated until a preset convergence condition is met; performing error
estimation and calculation according to a solving result to obtain a new step length, if an error meets a preset condition, advancing a
time step, updating the step length and a solution of the target nonlinear equation, otherwise, only updating the step length and returning to execute calculation of the Jacobian matrix. Second-order differential equations of specific categories can be solved more effectively, and stability, precision and efficiency of numerical calculation are improved.