Randomized trial demonstrates optimal error estimation in nonlinear Volterra integro-differential equations, suggesting enhanced accuracy in computational methods.
Key Points
This analysis aims to develop a reliable a posteriori error estimator for the discontinuous Galerkin method in solving nonlinear Volterra integro-differential equations.
Developed a residual-based error estimator for discontinuous Galerkin method.
Proved optimal convergence rates and superconvergence properties.
Constructed the estimator by solving local residual problems without initial conditions.
Achieved a convergence rate of O(h^(p+2)) for the error estimator under mesh refinement.
Demonstrated that the global effectivity index of the estimator approaches unity at O(h).
Illustrated accuracy and reliability through several numerical examples.