2023/12/02 by Dang, Trong D., Loc H. Nguyen, Nguyen, Loc H. +2 · 1 citation
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.2312.01179
openalex publication_date 2023/12/02 · openalex created_date 2023/12/07 · openalex updated_date 2026/07/28
This paper aims to determine the initial conditions for quasi-linear hyperbolic equations that include nonlocal elements. We suggest a method where we approximate the solution of the hyperbolic equation by truncating its Fourier series in the time domain with a polynomial-exponential basis. This truncation effectively removes the time variable, transforming the problem into a system of quasi-linear elliptic equations. We refer to this technique as the "time dimensional reduction method." To numerically solve this system comprehensively without the need for an accurate initial estimate, we used the newly developed Carleman contraction principle. We show the efficiency of our method through various numerical examples. The time dimensional reduction method stands out not only for its precise solutions but also for its remarkable speed in computation.