  A Kepler solver is an analytical method used to solve a two-body problem. In
this paper, we propose a new correction method by slightly modifying the Kepler
solver. The only change to the analytical solutions is that the obtainment of
the eccentric anomaly relies on the true anomaly that is associated to a unit
radial vector calculated by an integrator. This scheme rigorously conserves all
integrals and orbital elements except the mean longitude. However, the Kepler
energy, angular momentum vector and Laplace-Runge-Lenz vector for perturbed
Kepler problems are slowly-varying quantities. However, their integral
invariant relations give the quantities high-precision values that directly
govern five slowly-varying orbital elements. These elements combined with the
eccentric anomaly determine the desired numerical solutions. The newly proposed
method can considerably reduce various errors for a post-Newtonian two-body
problem compared with an uncorrected integrator, making it suitable for a
dissipative two-body problem. Spurious secular changes of some elements or
quasi-integrals in the outer solar system may be caused by short integration
times of the fourth-order Runge-Kutta algorithm. However, they can be
eliminated in a long integration time of 10^8 years by the proposed method,
similar to Wisdom-Holman second-order symplectic integrator. The proposed
method has an advantage over the symplectic algorithm in the accuracy but gives
a larger slope to the phase error growth.
