{"knowledge_schema": {"broad_category": "Mathematics \u2192 Numerical Methods \u2192 Finite Difference Methods", "refinement": "This problem pertains to the application of numerical methods for solving wave equations, specifically focusing on the transition from sequential to parallel algorithms.", "specific_scope": "The context involves the use of finite difference methods and parallel splitting techniques to enhance computational efficiency in higher-dimensional wave equations.", "goal": "Identify the crucial step necessary for converting a sequential algorithm into a parallel one in the context of numerical solutions for wave equations."}, "summary": "This question addresses the transition from sequential to parallel algorithms in the context of solving higher-dimensional wave equations using finite difference methods. The key step involves the use of linear partial fraction of fractional approximation, which is essential for effectively implementing parallel processing techniques. Understanding this transition is critical for improving computational efficiency in numerical simulations."}