What is Method: Definition and 1000 Discussions

In mathematics and computational science, the Euler method (also called forward Euler method) is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. It is the most basic explicit method for numerical integration of ordinary differential equations and is the simplest Runge–Kutta method. The Euler method is named after Leonhard Euler, who treated it in his book Institutionum calculi integralis (published 1768–1870).The Euler method is a first-order method, which means that the local error (error per step) is proportional to the square of the step size, and the global error (error at a given time) is proportional to the step size.
The Euler method often serves as the basis to construct more complex methods, e.g., predictor–corrector method.

View More On Wikipedia.org
Recent contents Top users
  1. lucasLima

    Can Newton's Method Solve This Non-Linear System Accurately?

    Homework Statement I'll try to be as clear as possible but this exercise is in portuguese and this is a free translation from me "The sum of two numbers is 3.4 .If we take each of them and summed with they square, the product of it would be 18.5856. The lowest of those number is in the interval...
  2. F

    Finite difference method derivation PDE

    Homework Statement Which algebraic expressions must be solved when you use finite difference approximation to solve the following Possion equation inside of the square : $$U_{xx} + U_{yy}=F(x,y)$$[/B] $$0<x<1$$ $$0<y<1$$ Boundary condition $$U(x,y)=G(x,y)$$ Homework Equations Central...
  3. R

    MHB Vedic Math Method: Prove Conjecture Inspired by a Math Trick

    Below is a conjecture that I can't prove. It was inspired by a math trick for division when the (base 10) denominator ends in the digit 9. Can anyone help me out with a proof? - - - Updated - - - Here is an excell example,
  4. karush

    MHB -206.q3.2 method of integrating factor

    2000 $\tiny{206.q3.2}\\$ $\textsf{3. use the method of integrating factor}\\$ $\textsf{to find the general solution to the first order linear differential equation}\\$ \begin{align} \displaystyle \frac{dy}{dx}+5y=10x \end{align} $\textit{clueless !}$
  5. Z

    Method of images: infinite line of charge above plate

    Homework Statement An infinite line of charge with charge density λ is parallel to and a distance d above an infinite grounded conducting plate. What is the charge density σ that is induced in the plate? For simplicity, consider the line of charge to lie along the line x = 0. Homework...
  6. S

    Root-Finding method in MATLAB

    Homework Statement Compute and plot the compressibility factor (y) verses pressure (x) for the (1) Van der Waal’s (2) Redlich-Kwong and (3) Peng-Robinson equations of state. Compressibility Factor, Z = (P*v)/(R*T); where v is the specific volume (V/v). Data for n-Butane: T = 500 K; Tc = 425.2...
  7. surya teja saithana

    Is my method of solving correct? is there any other method?

  8. Dong Aleta

    Standard method for identifying species in solid mixtures

    I want to know of any standard method for identifying (and possibly quantifying) the species contained in a solid mixture sample. Thanks in advance!
  9. Dtriction

    I Can this method be used to prove the Collatz Conjecture?

    There is a graph showing n on its x-axis and its total stopping time on its y axis. From here we can see that the points on the graph are not random at all; they have some kind of geometric pattern that is due to the 3x+1 in the odd case and x/2 in the even case. I have seen many attempts to...
  10. M

    Fortran I in Fortran please -- Bairstow's method & Newton-Raphson

    this is bairstow's method , i need to put Newton-raphson in a subroutine and i don't know what's wrong i keep getting the wrong answer when i execute please help parameter (np=100) parameter (eps=1e-3) real a(np) ,b(np),c(np) real r ,s ,ri,si integer n,i write(*,*)'n,r,s' read(*,*)n,r,s...
  11. karush

    MHB 205.q4.2 very painful Newton's Method

    %\section{Newton's Method } %\subsubsection{205.q4.2 } %\footnote{Leeward Community College}method m , $\textsf{a. Use Newton's Method: }$0000 \begin{align} \displaystyle x_{n+1}&=x_n-\frac{f(x_n)}{f'(x_n)} \end{align} $\textsf{b. Use Newton's Method to solve: }$ \begin{align}...
  12. H

    Adding Vectors using Cefore Method

    A bird is flying through the air with an air speed of 12.6 m/s heading 27.7° west of north. It is a windy day with the wind blowing at 8.95 m/s heading 12.5° south of west. What is the velocity of the bird as seen by a person on the ground? Note: I keep doing this question but my answer (the...
  13. Euler2718

    MATLAB "Linear Model" of a Pendulum via Euler's Method

    In my problem the linear modal is defined as the first term in the series expansion of \sin(x) so: \sin(x) = x - \frac{x^{3}}{3!}+\dots \sin(x) = x is the linear modal. So with this, I then have to write \frac{d^{2}x}{dt^{2}} = -\sin(x) as a system of x^{\prime} and y^{\prime}, so...
  14. S

    I Newton's method for approximating solutions of functions

    In my calculus textbook, it shows that a function's solution can be approximated using an approximated function tangent to the original function based on an approximated solution, where the equation to find the approximated is L(x) = f(X0) + f'(X0)*(X-X0), where when rearranged, gives x = Xo -...
  15. P

    MHB Finding Approximate Critical Number with Newton's Method

    Use Newton's Method to approximate a critical number of the function \displaystyle f(x) = \frac{1}{2} x^8 + \frac{6}{5} x ^5+ 2 x +10 near the point x = 2 . Use x_1 = 2 as the initial approximation. Find the next two approximations, x_2 and x_3, to four decimal places each.I have been...
  16. A

    Solving for Image Charges in Dielectrics

    Homework Statement The question is attached. Homework Equations The Attempt at a Solution I understand that the question would return to a typical conductor problem when ε2 >> ε1 so for the quadrant one, I placed image charges of q_1 at (d1 , 0 , -d2), -q1 at (-d1 , 0 , -d2) and another q1 at...
  17. MalachiK

    B How Do Jacobi Elliptic Functions Solve Nonlinear Differential Equations?

    I have ##\frac{d^2x(t)}{dt^2} + B(x(t))^3 = 0## for a system where I know the initial conditions and where B is a constant that's constructed from the properties of the system. I would like to find ##x(t)##. I've modeled the system in Python and produced some graphs. I know that ##x(t)## is...
  18. Angel Ochoa

    Different results with Explicit method and Implicit method

    Hello everybody, I´m simulating a problem of indentation of a tungsten needle tip on an aluminum layer. Before I was using just the module "Static Structural" from ANSYS, which is based on an implicit solver. Now I wanted to do the same simulation with the module "Explicit Dynamics" of ANSYS...
  19. Jackson Lee

    EM waves and traditional method of transmission

    Hey, guys. We all know power of AC currents is transferred via EM waves, but we seldom use that to calculate power in AC system. The reason for this is wavelength is very long. I want to know if there is really existed a transmission line which is 500km, just the length of EM wavelength, then...
  20. T

    Probability of Getting at Least One Card from Each Suit

    Hi all I am have a problem with this question I have used two method to solve and get two different ans, could someone please point where I am going wrong Homework Statement Five cards are dealt from a standard shuffled deck. What is the probability that: There is at least one card from each...
  21. F

    MHB Question regarding pigeonhole method , number induction

    Hi i have few questions over here and need some expert/pro view with approaching the question. The proving one would be an issue to me as well. Hope people would be able to assist me here , because i am basically struggling with it :( thanks Questions : My Working : No idea how to...
  22. M

    Help with Drawing Momentum with Virtual Method

    Hello guys I'm struggling a bit with drawing momen/[M_o], to this "frame". I will be using virtual Method. So, could you you have corrected me if it's wrong?
  23. thunderstrike33

    Writing Vector Loops and Geometric Constraints for a Mechanism with a P1 Joint

    How would you write the vector loops and geometric constraints for this mechanism?
  24. G

    Guidance or tutorial of applying pseudo-material method

    Hi, I'm working on a project of coupled simulation involving MCNP and Fluent, and having trouble with how to apply the pseudo-material method in cross section handling. Is there any related material or tutorial? Or, does anyone know the procedure of applying the method and what kind of files the...
  25. A

    I Finite difference method for Schrödinger equation

    Suppose I want to solve the time-independent Schrödinger equation (ħ2/2m ∂2/∂x2 + V)ψ = Eψ using a numerical approach. I then discretize the equation on a lattice of N points such that x=(x1,x2,...,xN) etc. Finally I approximate the second order derivative with the well known central difference...
  26. karush

    MHB What is the answer after convergence in TI-Nspire CX CAS?

    $\text{Evaluate answer from }\textit{ TI-Nspire CX CAS}$ \begin{align*} \displaystyle S_k&=\sum_{k=1}^{\infty} \left[\frac{(-2)}{9^{k+1}}\right] =\frac{-2}{99} \\ \end{align*} ok wasn't sure what weapon of choice to use $\tiny{206.10.3.75}$ ☕
  27. nysnacc

    Efficient Techniques for Solving Second Order Differential Equations

    Homework Statement Homework EquationsThe Attempt at a Solution Should I find the characteristic equation then find the solution y2? Or just integrate the expression of part (a)?? Part B, just find the derivatives and plug into the ode
  28. parshyaa

    B Measurements of angles in circular method

    Why θ in radian equals arc/radius? I know that it can't be proved but there must be a explanation for this formula. How founder may have got this idea.
  29. toforfiltum

    Newton's method to approximate critical point

    Homework Statement Let ##F(x,y)=4sin(xy)+x^3+y^3## Use Newton's method to approximate the critical point that lies near ##(x,y)=(-1,-1)## Homework EquationsThe Attempt at a Solution I have a problem here because the derivative is not a square matrix. Hence, I can't find the inverse needed for...
  30. T

    MHB Identifying Vertical Asymptotes: A Non-Factoring Method

    im stuck on identifying vertical asymptotes because of this nasty denominator. My professor telling me to factor it out but, is there different way to solve for the vertical asymptotes.
  31. ramzerimar

    I Finite Element Method: Weak form to Algebraic Equations?

    Okay, I'm following a series of video lectures on applications of finite element method to engineering, and the tutor started by demonstrating the mathematical background of FEM using a simple heat transfer problem. He derived the governing equation (in just one dimension): (1)...
  32. K

    B Euler's method for second order DE

    Can the Euler approximation method be used to solve higher order DE? I have ##\ddot x=\omega^2 x## which i rewrite as ##y''=\omega^2y##. initial conditions y(0)=0, y'(0)=1. The Euler method: ##y_{n+1}=y_n+h\cdot y'_n##. i use this to make: $$y''_{n+1}=y'_n+h\cdot...
  33. King_Silver

    Height of Instrument (Leveling method)

    I recently did a level survey however am a little stumped over a calculation. I am trying to calculate the Reduced Level using the "Height of Instrument" method. I know how to do the calculations etc. so I am not asking for this to be done for me. It is more of a general question about this sort...
  34. M

    Method to calculate work while moving two walls

    Hi guys, It is not some homework, so I think it is better to post here. I would like to know if my method is correct for the work of the walls x and y. I suppose no mass, no friction and the gas keeps its temperature constant. An external device modify the shape of a triangle but it keeps...
  35. M

    I Linear least-squares method and row multiplication of matrix

    Suppose that I have an overdetermined equation system in matrix form: Ax = b Where x and b are column vectors, and A has the same number of rows as b, and x has less rows than both. The least-squares method could be used here to obtain the best possible approximative solution. Let's call this...
  36. John_Blacktower

    A Pseudospectral method using FFT to solve diff equation

    Hello everyone, I'm trying to solve by FFT a convection diffusion eqaution on a 3 D box with an slit condition on z-axix and periodic conditions on x and y axis. ∂C/∂t=D∇[2]C-v⋅∇C (1) v=vx + vy + vz i have solved the velocity of fluid, i mean a really know what is the velocity of flow field...
  37. L

    B Forgotten correct method of basic arithmetic (subtraction)

    What happens when you have to subtract: 30 -9 Basically 30 - 9 but the 3 must be made 13, so what happens to the zero? I know if it was any other number we would reduce its value by one. Also, if possible, can anyone please show me how 30 in base 5 is 110? I understand that its 1*5*5 + 1*5...
  38. J

    MHB Solving a Disk Method Problem: What Info Needed?

    So I am trying to find the volume of a solid with this information given to me: 𝑥=0 𝑦=0 𝑦=−2𝑥+2 However, when I go to enter this information into a disk method calculator, I don't have enough information to enter into the calculator, such as the lower function and limits. My question is...
  39. Marcin H

    Engineering Bridge/Ladder Circuit and Node Voltage Method

    Homework Statement Homework Equations Node Voltage Method V=IR The Attempt at a Solution So I have never worked with a bridge/ladder circuit before and I am not sure if I am doing it correctly. My professor never gave us an example of a bridge/ladder so I'm kinda winging it. Anyway can I...
  40. S

    Which method is correct for this problem involving motion of

    My Approach is shown in the picture.
  41. A

    I K dot p method with SO interaction

    I am trying to derive the k dot p formula with the spin orbit interaction term included. I am having some trouble. I insert a bloch wave function multiplied with an unspecified spinor. But how do I treat the cross product term that comes from the SO and what is the effect of the pauli matrix...
  42. S

    Finite Element Method: Find Total Mass Matrix of Coupled Element

    Does anyone know how to find the total mass matrix of two coupled element by using Finite Element Method?
  43. W

    Rayleigh method Dimensional Analysis

    Homework Statement ii)Rayleigh method gives me inverse of expected result.Would really appreciate your help. Homework Equations show that ##f(gamma)##=##(\frac {ro*R^5} {E*t^2})## where ro=density R=radius E=energy The Attempt at a Solution We will do dimensional analysis on the elements...
  44. A

    How can I draw a line in assembly language without using decimal numbers?

    i have a frame-buffer , and i want to draw a line using assembly language . i cannot work with decimal numbers . what's the best and most efficient method ? thank you .
  45. G

    Direct Stiffness Method for Analyzing Tripod Frame with Equally Spaced Legs

    Let's say you have part of frame contacting the ground, such as the feet on the base of the tripod. Assuming each leg is equally spaced around a center post, how would you go about analyzing this type of structure? I'm trying to teach myself how to use the stiffness method, but all the examples...
  46. Srismiles

    A Four Probe Method: Why 0-200mV & 0.20mA?

    Why we use 0 to 200 mv and 0 to 0.20 ma in four probe method and also why we use only mercury thermometer in this method?
  47. F

    Ambiguity in the method applied for differential equations

    Homework Statement Why do we need two solutions to solve a 2nd order linear differential equation? lets consider a differential equation with equal roots for auxiliary equation. So the reasoning behind why can't we use y=Aen1x+Ben2x as its general solution is because since the roots are equal...
  48. D

    I Generating polynomials for a multistep method

    Hi, I'm struggling to understand how the generating polynomials work and are implemented in the difference equation for a general ODE y' = f(t,y) Difference Equation Generating polynomials "Coefficients are normalized either by a_k = 1 or sigma(1) = 1
  49. D

    Stability function for a basic RK method

    Homework Statement Hi, can someone explain how they get this stability function. Homework Equations http://blob:http://imgur.com/840ee1fe-f09c-49ab-bdbb-7f953777f900 The Attempt at a Solution I have attempted to do it two ways, and I'm not sure if I'm just having an awfully bad day at maths...
  50. Leonardo Machado

    Problems with Runge-Kutta method

    I'm writing a program to compute an ODE solution of the Kepler's problem based on Runge-Kutta 4th order method and today I've past the whole day trying to made it work, but I've failed, maybe you could help me to kill the problem ? The solutions is cartesian. int main(){ int n...
Back
Top