Construction and numerical resolution of high-order accuracy decomposition scheme for a quasi-linear evolution equation

In the present work the Cauchy problem for an abstract evolution equation with a Lipschitz-continuous operator is considered, where the main operator represents the sum of positive definite self-adjoint operators. The fourth-order accuracy decomposition scheme is constructed for an approximate solution of the problem. The theorem on the error estimate of an approximate solution is proved. Numerical calculations for different model problems are carried out using the constructed scheme. The obtained numerical results confirm the theoretical conclusions.