Her first book published in 1953 called Mixed Problems for a Hyperbolic Equation used the finite difference method to prove theoretical results mainly the solvability of initial boundaryvalue problems for general secondorder hyperbolic equations

Could you correct the punctuation please?
Her first book published in 1953 called Mixed Problems for a Hyperbolic Equation used the finite difference method to prove theoretical results, mainly the solvability of initial boundary-value problems for general second-order hyperbolic equations.