Neural networks have been widely used to solve partial differential equations (PDEs) in different fields, such as biology, physics, and materials science. Although current research focuses on PDEs ...
Euler Method: The simplest numerical method for solving ODEs, which uses the derivative to project forward. [ y_{n+1} = y_n + h \cdot f(x_n, y_n) ] Heun's Method (Improved Euler Method): A two-step ...
ABSTRACT: Optimal boundary control of semilinear parabolic equations requires efficient solution methods in applications. Solution methods bypass the nonlinearity in different approaches. One approach ...
The paper deals with the computation of functions of fractional powers of differential operators. The spectral properties of these operators naturally suggest the use of rational approximations. In ...
Introduction: Fractional diffusion equations offer an effective means of describing transport phenomena exhibiting abnormal diffusion pat-terns, often eluding traditional diffusion models. Methods: We ...
Abstract: Recently, many deferential evolution-based algorithms have been developed to solve constrained optimization problems. The performance of these methods outperforms the performance of single ...
In this article a new approach is considered for implementing operator splitting methods for transport problems, influenced by electric fields. Our motivation came to model PE-CVD (plasma-enhanced ...
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