Steffensen's Method for Systems of Nonlinear Equations
Generalized Steffensen's Method for Simultaneous Nonlinear Systems originally credited to J. F. Traub. Video shows how to solve nonlinear systems by approximating the Jacobian. Example code on GitHub https://www.github.com/osveliz/numerical-veliz Chapters 0:00 Prerequisites 0:20 Intro 0:
From playlist Solving Systems of Nonlinear Equations
Steffensen's Method with Aitken's Δ²
Discussion of Steffensen's Method and Aitken's Delta-Squared Method with their relation to Fixed Point Iteration including examples, convergence acceleration, order, and code. GitHub: https://github.com/osveliz/numerical-veliz Chapters 0:00 Intro 0:08 Aitken's Δ² Method History 0:23 Deriv
From playlist Root Finding
Generalized Aitken-Steffensen Method
Generalized Aitken's delta-squared method and Generalized Steffensen's Method applying Fixed Point Iteration to Systems of Nonlinear Equations. Video goes step-by-step to derive Generalized Aitken-Steffensen and discusses induced and accelerated convergence behavior as well as quadratic or
From playlist Solving Systems of Nonlinear Equations
Graeffe's Root-Squaring Method (also called Graeffe-Dandelin-Lobachevskiĭ or Dandelin–Lobachesky–Graeffe method) for finding roots of polynomials. The method solves for all of the roots of a polynomial by only using the coefficients and does not require derivatives nor an interation funct
From playlist Root Finding
Euler’s method - How to use it?
► My Differential Equations course: https://www.kristakingmath.com/differential-equations-course Euler’s method is a numerical method that you can use to approximate the solution to an initial value problem with a differential equation that can’t be solved using a more traditional method,
From playlist Differential Equations
C34 Expanding this method to higher order linear differential equations
I this video I expand the method of the variation of parameters to higher-order (higher than two), linear ODE's.
From playlist Differential Equations
[Calculus] Newton's Method || Lecture 36
Visit my website: http://bit.ly/1zBPlvm Subscribe on YouTube: http://bit.ly/1vWiRxW Hello, welcome to TheTrevTutor. I'm here to help you learn your college courses in an easy, efficient manner. If you like what you see, feel free to subscribe and follow me for updates. If you have any que
From playlist Calculus 1
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
Wegstein Method for finding roots, accelerating fixed point iteration, and inducing convergence in fixed point iteration. Explained examples and discussion of order as well as how to compute q. Example code: https://github.com/osveliz/numerical-veliz Chapters 0:00 Intro 0:22 Wegstein's Me
From playlist Root Finding
Fixed Point Iteration method for finding roots of functions. Frequently Asked Questions: Where did 1.618 come from? If you keep iterating the example will eventually converge on 1.61803398875... which is (1+sqrt(5))/2. Why not use x = x^2 -1? Generally you try to reduce the degree of the
From playlist Root Finding
Converge order and error reduction can be confusing but this video breaks it down and provides examples showing how order relates to speed and runtime. It also explains how order of convergence relates to Big O. Watching the other videos on this channel can be helpful but is not necessary.
From playlist Root Finding
Fixed Point Iteration Method followup video answering your frequently asked questions like "How do you pick a starting point?" and "How do you use the convergence test without the root?" Example code can be found at https://github.com/osveliz/numerical-veliz specifically in the programs fo
From playlist Root Finding
Euler's method for solving non-separable differential equation by approximation.
From playlist Advanced Calculus / Multivariable Calculus
B01 An introduction to numerical methods
Most differential equations cannot be solved by the analytical techniques that we have learned up until now. I these cases, we can approximate a solution by a set of points, by using a variety of numerical methods. The first of these is Euler's method.
From playlist A Second Course in Differential Equations
Fixed Point Iteration System of Equations with Banach
Fixed Point Iteration Method to solve Systems of Nonlinear Equations with discussion of Banach Fixed Point Theorem, finding the Jacobian, convergence, and order. Example code on GitHub: http://github.com/osveliz/numerical-veliz Chapters: 00:00 Intro 00:25 Systems of Equations 00:33 Solvin
From playlist Solving Systems of Nonlinear Equations
Solving a trigonometric equation with applying pythagorean identity
👉 Learn how to solve trigonometric equations. There are various methods that can be used to evaluate trigonometric equations, they include factoring out the GCF and simplifying the factored equation. Another method is to use a trigonometric identity to reduce and then simplify the given eq
From playlist Solve Trigonometric Equations by Factoring
Generalized False Position & Alternative Secant Methods
False Position Method for Nonlinear Systems (aka Generalized Regula Falsi) along with two Alternative Secant Methods. Includes discussion of history and primary sources along with numeric examples and visualizations. Example code hosted on GitHub https://github.com/osveliz/numerical-veliz
From playlist Solving Systems of Nonlinear Equations