Numerical differential equations
Finite-difference time-domain (FDTD) or Yee's method (named after the Chinese American applied mathematician Kane S. Yee, born 1934) is a numerical analysis technique used for modeling computational electrodynamics (finding approximate solutions to the associated system of differential equations). Since it is a time-domain method, FDTD solutions can cover a wide frequency range with a single simulation run, and treat nonlinear material properties in a natural way. The FDTD method belongs in the general class of grid-based differential numerical modeling methods (finite difference methods). The time-dependent Maxwell's equations (in partial differential form) are discretized using central-difference approximations to the space and time partial derivatives. The resulting finite-difference equations are solved in either software or hardware in a leapfrog manner: the electric field vector components in a volume of space are solved at a given instant in time; then the magnetic field vector components in the same spatial volume are solved at the next instant in time; and the process is repeated over and over again until the desired transient or steady-state electromagnetic field behavior is fully evolved. (Wikipedia).
Finite Difference Method for finding roots of functions including an example and visual representation. Also includes discussions of Forward, Backward, and Central Finite Difference as well as overview of higher order versions of Finite Difference. Chapters 0:00 Intro 0:04 Secant Method R
From playlist Root Finding
Approximating the Jacobian: Finite Difference Method for Systems of Nonlinear Equations
Generalized Finite Difference Method for Simultaneous Nonlinear Systems by approximating the Jacobian using the limit of partial derivatives with the forward finite difference. Example code on GitHub https://www.github.com/osveliz/numerical-veliz Chapters 0:00 Intro 0:13 Prerequisites 0:3
From playlist Solving Systems of Nonlinear Equations
Find a General Solution to a Nonhomogeneous DE Using Undetermined Coefficients (Repeat Term)
This video explains how to determine the general solution to a linear second order differential equation using the method of undetermined coefficients. http://mathispower4u.com
From playlist Linear Second Order Nonhomogeneous Differential Equations: Method of Undetermined Coefficients
Find a General Solution to a Nonhomogeneous DE Using Undetermined Coefficients (Quadratic)
This video explains how to determine the general solution to a linear second order differential equation using the method of undetermined coefficients. http://mathispower4u.com
From playlist Linear Second Order Nonhomogeneous Differential Equations: Method of Undetermined Coefficients
Determine a Particular Solution of a Second Order DE using Variation of Parameters
This video provides an example of how to find a particular solution of a linear second order nonhomogeneous differential equation using the method of variation of parameters. Site: http://mathispower4u.com
From playlist Linear Second Order Nonhomogeneous Differential Equations: Variation of Parameters
Find a General Solution to a Nonhomogeneous DE Using Undetermined Coefficients (Linear)
This video explains how to determine the general solution to a linear second order nonhomogeneous differential equation using the method of undetermined coefficients. http://mathispower4u.com
From playlist Linear Second Order Nonhomogeneous Differential Equations: Method of Undetermined Coefficients
Find a General Solution to a Nonhomogeneous DE Using Undetermined Coefficients (Exponential)
This video explains how to determine the general solution to a linear second order differential equation using the method of undetermined coefficients. http://mathispower4u.com
From playlist Linear Second Order Nonhomogeneous Differential Equations: Method of Undetermined Coefficients
Find a General Solution to a Nonhomogeneous DE Using Undetermined Coefficients (Sine)
This video explains how to determine the general solution to a linear second order differential equation using the method of undetermined coefficients. http://mathispower4u.com
From playlist Linear Second Order Nonhomogeneous Differential Equations: Method of Undetermined Coefficients
Ex 2: Method of Undetermined Coefficients to Find the General Solution (quadratic)
This video provides an example of how to find the general solution to a linear second order nonhomogeneous differential equation using the method of undetermined coefficients. Site: http://mathispower4u.com
From playlist Linear Second Order Nonhomogeneous Differential Equations: Method of Undetermined Coefficients
Lecture 15 (CEM) -- Finite-Difference Time-Domain
This lecture introduces the finite-difference time-domain method. It includes the basic method, derivation of the update equations, and some implementation issues such as Fourier transforms and calculation of transmittance and reflectance. This lecture is NOT intended to leave the studen
From playlist UT El Paso: CEM Lectures | CosmoLearning.org Electrical Engineering
Ari Stern: Hybrid finite element methods preserving local symmetries and conservation laws
Abstract: Many PDEs arising in physical systems have symmetries and conservation laws that are local in space. However, classical finite element methods are described in terms of spaces of global functions, so it is difficult even to make sense of such local properties. In this talk, I wil
From playlist Numerical Analysis and Scientific Computing
MIT 10.34 Numerical Methods Applied to Chemical Engineering, Fall 2015 View the complete course: http://ocw.mit.edu/10-34F15 Instructor: James Swan This is a review session to help prepare the quiz. Later, students moved on to learn finite volume methods and constructing simulations of PD
From playlist MIT 10.34 Numerical Methods Applied to Chemical Engineering, Fall 2015
Marta D'Elia: A coupling strategy for nonlocal and local models with applications ...
The use of nonlocal models in science and engineering applications has been steadily increasing over the past decade. The ability of nonlocal theories to accurately capture effects that are difficult or impossible to represent by local Partial Differential Equation (PDE) models motivates a
From playlist HIM Lectures: Trimester Program "Multiscale Problems"
Lecture 1 (CEM) -- Introduction to CEM
This lecture introduces the course and steps the student through an overview of most of the major techniques in computational electromagnetics.
From playlist UT El Paso: CEM Lectures | CosmoLearning.org Electrical Engineering
Mod-01 Lec-23 Discretization of ODE-BVP using Least Square Approximation and Gelarkin Method
Advanced Numerical Analysis by Prof. Sachin C. Patwardhan,Department of Chemical Engineering,IIT Bombay.For more details on NPTEL visit http://nptel.ac.in
From playlist IIT Bombay: Advanced Numerical Analysis | CosmoLearning.org
Numerical Homogenization by Localized Orthogonal Decomposition (Lecture 2) by Daniel Peterseim
DISCUSSION MEETING Multi-Scale Analysis: Thematic Lectures and Meeting (MATHLEC-2021, ONLINE) ORGANIZERS: Patrizia Donato (University of Rouen Normandie, France), Antonio Gaudiello (Università degli Studi di Napoli Federico II, Italy), Editha Jose (University of the Philippines Los Baño
From playlist Multi-scale Analysis: Thematic Lectures And Meeting (MATHLEC-2021) (ONLINE)
Erik Burman: Combining cut element methods and hybridization
Recently there has been a surge in interest in cut, or unfitted, finite element methods. In this class of methods typically the computational mesh is independent of the geometry. Interfaces and boundaries are allowed to cut through the mesh in a very general fashion. Constraints on the bou
From playlist Numerical Analysis and Scientific Computing
Small deformations of biomembranes
Charlie Elliott University of Warwick, UK
From playlist 2018 Modeling and Simulation of Interface Dynamics in Fluids/Solids and Their Applications
Find a Particular Solution to a Nonhomgeneous DE Using Variation of Parameters
This video explains how to determine a particular solution to a linear second order differential equation using the method of variation of parameters. http://mathispower4u.com
From playlist Linear Second Order Nonhomogeneous Differential Equations: Variation of Parameters
Numerical Hydrodynamics: Part 2 by Ian Hawke
PROGRAM: GRAVITATIONAL WAVE ASTROPHYSICS (ONLINE) ORGANIZERS : Parameswaran Ajith, K. G. Arun, Sukanta Bose, Bala R. Iyer, Resmi Lekshmi and B Sathyaprakash DATE: 18 May 2020 to 22 May 2020 VENUE: Online Due to the ongoing COVID-19 pandemic, the original program has been cancelled. Howe
From playlist Gravitational Wave Astrophysics (Online) 2020