On the Faedo–Galerkin Method for Non-autonomous Nonlinear Differential Systems

This article contemplates a non-autonomous nonlinear differential system in a separable Hilbert space 𝒳 . The projection operators are used to confine our concern to a finite-dimensional subspace of 𝒳 . The existence, uniqueness, and convergence of approximate solutions are explored by making use of the hypothesis of fractional powers of a closed linear operator. We also analyze the Faedo–Galerkin approximation of the solution. An example is also built to exhibit the significance of the acquired results.