Physics and Python stuff. Most of the videos here are either adapted from class lectures or solving physics problems. I really like to use numerical calculations without all the fancy programming ...

Physics and Python stuff. Most of the videos here are either adapted from class lectures or solving physics problems. I really like to use numerical calculations without all the fancy programming ...

Abstract: We consider the problem of finding an input signal which transfers a linear boundary controlled 1-D parabolic partial differential equation with spatially varying coefficients from a given ...

Abstract: Physics-Informed Neural Networks (PINN) has surged in popularity within deep learning. However, automatic differentiation (AD) based PINN may encounter inaccuracies in the explicit ...

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 ...

Introduction: Fractional diffusion equations offer an effective means of describing transport phenomena exhibiting abnormal diffusion pat-terns, often eluding traditional diffusion models. Methods: We ...

Together with electroencephalography (EEG), magnetoencephalography (MEG) is a technique used to investigate brain activity. EEG and MEG are devoted to detect the electric potential distribution and ...

ABSTRACT: In this paper, we implement the spectral collocation method with the help of the Legendre poly-nomials for solving the non-linear Fractional (Caputo sense) Klein-Gordon Equation (FKGE). We ...