This book introduces a comprehensive mathematical formulation of the three-dimensional ocean acoustic propagation problem by means of functional and operator splitting techniques in conjunction with rational function approximations. It presents various numerical solutions of the model equation such as finite difference, alternating direction and preconditioning. The detailed analysis of the concept of 3D, N x 2D and 2D problems is very useful not only mathematically and physically, but also computationally. The inclusion of a complete detailed listing of proven computer codes which have been in use by a number of universities and research organizations worldwide makes this book a valuable reference source. Advanced knowledge of numerical methods, applied mathematics and ocean acoustics is not required to understand this book. It is oriented toward graduate students and research scientists to use for research and application purposes.Contents: IntroductionBasic Mathematical Model DevelopmentsA Pseudopartial Differential EquationA High-Order Wave EquationEnhancement of the High-Order Wave EquationNumerical Accuracy Test: An Analytic SolutionThree-Dimensional EffectsThe Computer Model — FOR3DReadership: Scientists, engineers and students in ocean acoustics.Key Features:Forty years after its appearance and subsequent developments, the first comprehensive treatment showing the present state of the subject is welcomeAntieigenvalue analysis revealed that the celebrated Kantorovich convergence rates for optimization in numerical analysis and economics are exactly operator-trigonometricIn quantum mechanics, one of the great developments was John Bell's formulation of his inequalities to test the Einstein–Podolsky–Rosen hidden variable theory. Gustafson's antieigenvalue operator trigonometry has provided a new geometrical viewpoint which significantly clarified the mathematical and physical meanings of the Bell Inequalities