Numerical Analysis on Quantum Graphs Differential/Pseudo-Differential Operator: Some Basic Structure

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Abstract

We analyze the numerical solution of boundary and initial value problems for differential equations presented on graphs or networks. The graphs of intrigue are quantum graphs, i.e., metric graphs blessed with a differential operator following up on capacities characterized on the graph's edges with reasonable side conditions. We depict and examine the utilization of linear limited components to discretize the spatial subsidiaries for a class of linear elliptic model problems. Boolean algebra shapes a foundation of computer science and digital system outline. Numerous issues in digital rationale outline and testing, artificial intelligence, and combinatory can be communicated as a succession of tasks on Boolean capacities. In this day and age computers are once in a while remaining solitary. They are regularly associated with systems that can change in size from little to colossal.