Method Definition and 1000 Threads

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
  1. C

    MHB What statistical method to use for the below problem?

    I want to know which statistical method to use for the below problem. Suppose I have the revenue data of 5 companies in the same industry. And, also the market share of the industry. I calculated the ratio of all against each other. Now, with the above calculation, i want to find out which among...
  2. M

    Simplified Method of Combustion Turbine Supercharging

    I have been interested in (the concept of) large frame industrial combustion turbine supercharging since the early 90's. However, although I believe the concept has merit and has been done successfully in at least one location nearly 3 or 4 decades ago, the concept has not evolved since...
  3. L

    Transfer Matrix Method for 2D Ising & Other Models

    You can use transfer matrix method for 2d Ising model. Is there a list of models for which this method could be of use. Such as classical Heisenberg perhaps? Or Potts?
  4. J

    Finite Differences-Semi discretization method on Heat Equation

    Hi!, I'm working on a personal project: Solve the heat equation with the semi discretization method, using my own Mathematica's code, (W. Mathematica 9). The code: I'm having problems with the variable M (the number of steps). It works with M=1-5, but no further, I do not know what's going...
  5. J

    Assistance with adaptive time step for Dormand Prince Method

    Homework Statement I am trying to create a MATLAB program that propagates the solar system when given initial velocity and position. I have successfully implemented a Runge-Kutta 4th order integrator but would like to see the difference when moving to an adaptive time step method. I think my...
  6. M

    What is the method of moment estimator for θ?

    Homework Statement Let ##X_1, X_2, ..., X_n## be a random sample from ## f_θ=2x/θ^2## , ##0≤x≤θ##. Find a maximum likelihood estimator for θ. Find the method of moment estimator for θ. The Attempt at a Solution I have already found that the MLE is max{##x_i##}. I just need to find the...
  7. F

    MHB How do I evaluate the contour integral for $f'(z)/f(z)$ around $|z|=4$?

    Let $f(z)=\frac{(z^2+1)^2}{(z^2+2z+2)^3}$ . Evaluate the contour integral of $f'(z)/f(z)$ around the circle $|z|=4$? How do I do this without having to find $f'(z)$? Thanks
  8. V

    The right method to put an oil seal in a housing

    i have a question, when i put a oil seal in a housing, should i put grease between the housing and the oil seal? because that is more easy to out in. Can explain the theory to me please?
  9. Greg Bernhardt

    Exploring CORDIC Algorithm: Digit-by-Digit Method & Volder's Algorithm

    Definition/Summary CORDIC (digit-by-digit method, Volder's algorithm) (stands for COordinate Rotation DIgital Computer) is a simple and efficient algorithm to calculate hyperbolic and trigonometric functions. It is commonly used when no hardware multiplier is available as the only operations...
  10. M

    Runge-Kutta Method - Need help with the calculus

    When deriving the Runge-Kutta Method to solve y'=f(x) we need to use Taylor expansion. Hence we need to differentiate the function many times. y'(x)=f(y(x)) y''(x)=f'(y(x))y'(x) = f'(y(x))f(y(x)) y''' = f''(y(x))(f(y(x)),y'(x)) + f'(y(x))f'(y(x))y'(x) I can understand the second...
  11. A

    Algorithms for atmospheric water balance method

    Hi I want to estimate divergence of water vapor flux in atmosphere with NCEP/NCAR data I have the equations for that and i want the algorithms to implement it for NCEP/NCAR data. I have a paper with algorithms for ECMWF data. Can i take this? or it required new algorithms for my data
  12. P

    Setting up the Lagrangian Multipliers method for spherical coords

    This isn't really a homework question, but may be similar to a typical example problem so I posted it here. Homework Statement I want to find the max and min dot product of a 3d vector and all points in a sphere constrained by angles in spherical coordinates. Homework Equations A point...
  13. S

    How is the Inverse Phasor Transform of Sum of Individual Phasors Proven?

    Hello, Can someone show me how the inverse Phasor transform of the sum of individual Phasors of sinusoidal functions of the same frequency is the sum of the sinusoids? I could not find any rigorous proof and help appreciated. Thanks.
  14. I

    MHB Estimate $y(0.5)$ using Euler's Method

    use euler's method with step size 0.1 to estimate y(0.5), where y(x) is the solution of the initial-value problem y'=y(x+1), y(0)=1. round your answer to four decimal places. this is all I've done so far $y'=y(x+1)$ $y(0)=1$ $h=0.1$ $x_{0}=0$ $y_{0}=1$ $x_{1}=x_{0}+h=0+0.1=0.1$...
  15. C

    Is It Possible to Use the Method of Undetermined Coefficients Here?

    I'm doing a practice problem I found online, and I get a solution, but I think it should have a sine term in it. I looked up the solution, and most sites say to use variation of parameters, but is it possible to use the method of undetermined coefficients? The problem is as follows: y'' + 4y...
  16. M

    Impact of trolley - hand calculation method

    Hello, Been a while since I posted on here, nice to be back :) . I just want some pointers as to the methodology for an impact load case that I'm looking at. I've attached a very basic sketch of a trolley which is traveling at a known velocity and impacts a rigid structure at it's base. What...
  17. E

    Why do we get oscillations in Euler's method of integration and what i

    When using Euler's method of integration, applied on a stochastic differential eq. : For example - given d/dt v=−γvΔt+sqrt(ϵ⋅Δt)Γ(t) we loop over v[n+1]=v[n]−γv[n]Δt+sqrt(ϵ⋅Δt)Γn. (where −γv[n] is a force term, can be any force and Γn is some gaussian distributed random variable. ) . Then if...
  18. D

    Converting MPa·mm1/2 to MPa.m1/2: A Scientific Approach

    I need to convert 12.5 MPa·mm1/2 into MPa.m1/2. I am unsure on how to do this, my two guesses are as follows: 1. (12.5) / ( 1 / 10001/2) = 395.28 MPa.m1/2 2. (12.5) / (12.5 / 10001/2) = 31.62 MPa.m1/2 Is either of those correct? Thanks!
  19. C

    MHB FE 1D method and hat functions

    Hi all, I'm doing a project on the finite elements method and am struggling to understand a part of it. I have defined the hat functions as: \[ \phi_i(x) = \begin{cases} \frac{x-x_{i-1}}{h} & \text{if } x_{i-1}\leq x<x_i \\ \frac{x_{i+1}-x}{h} & \text{if } x_i\leq x<x_{i+1}\\ 0 &...
  20. A

    Why Does Initial Approximation Affect Convergence Speed in Newton's Method?

    Homework Statement Use Newton's method with x1 = 1 to find the root of the equation x3 - x = 1 to correct six decimal places. Do the question again with x1 = 0.6 Do the question again with x1 = 0.57 You probably need to do it in an excel sheet. With each try, it takes longer to...
  21. H

    Structural Dynamics Analysis - Modal method or time integration?

    Hi all, I need help with numerical solution of motion equation. From the numerical point of view and in the real of the finite element method, which method is recommended for the solution of damped ( proportional damping) linear motion equation? I have been trying three common methods; Modal...
  22. R

    Iteration method for density equations

    hi there; I need some help with the following formulas In the interaction picture. ##\frac{d}{dt}\rho(t)=\frac{1}{i\hbar}[V(t),\rho(t)]## (1) Then ##\rho(t+\Delta t) = \rho(t)+\frac{1}{i\hbar}\int_t^{t+\Delta t} dt' [V(t'),\rho(t')]## (2) This equation can be iterated. and...
  23. T

    FE method, how ? (software Comsol)

    Hi all, The plastic flow rule for large strains in a continuum medium can be written as : -\dfrac{1}{2} \Big ( \dfrac{d}{dt}(F_p^{-1} ). ^t F_p^{-1} + F_p^{-1} . ^t \dfrac{d}{dt} ( F_p^{-1} ) \Big)= \lambda F^{-1} \dfrac{\partial f}{\partial \tau} F F_p^{-1} . ^t F_p^{-1} where F_p is the...
  24. R

    Programs Free online introductory classes good method of choosing an eng.major?

    I am an upcoming freshman. I will major in engineering. When applying to the school I chose mechanical because of its "versatility and stability in the job market." (I don't fully understand the meaning of these phrases; I get my knowledge from anecdotal experience when browsing forums). I may...
  25. W

    Newton-Raphson Method for Non-linear System of 3 variables in Matlab

    I am trying to solve 3 non-linear system of 3 variables using the Newton-raphson method in matlab. Here are the 3 non-linear equations: \begin{equation} c[\alpha I+ k_f+k_d+k_ns+k_p(1-q)]-I \alpha =0 \end{equation} \begin{equation} s[\lambda_b c P_C +\lambda_r (1-q)]- \lambda_b c P_C =0...
  26. A

    MHB Deriving potential energy by simulation method

    The picture shows the potential due to ring charge. Please show the full steps of deriving the equation of electrical potential. I don't know how to start at all. NOTE: The electric potential of the revolving symmetrical ring electric charge related to the axis z as depicted in the diagram...
  27. R

    MATLAB Newton-Raphson Method for Non-linear System of 3 variables in Matlab

    I am trying to solve 3 non-linear system of 3 variables using the Newton-raphson method in matlab. Here are the three equations: \begin{equation} c[\alpha I+ k_f+k_d+k_ns+k_p(1-q)]-I \alpha =0 \end{equation} \begin{equation} s[\lambda_b c P_C +\lambda_r (1-q)]- \lambda_b c P_C =0 \end{equation}...
  28. M

    MHB Method of characteristics-How can I continue?

    Hey! :o I have to solve the following hyperbolic system of equations using the method of characteristics: $$\left.\begin{matrix} \frac{\partial{u_1}}{\partial{t}}+\frac{\partial{u_1}}{\partial{x}}+x^2 \frac{\partial{u_2}}{\partial{x}}=0\\ \frac{\partial{u_2}}{\partial{t}}+t^2...
  29. S

    MHB How Do You Apply the Washer Method Correctly?

    Just doing the Washer Method for now, once that's sorted out I'm going to see if I can do the Shell Method. I just want to be sure I'm doing this right here. That's x=0, y=2, y=5-x This is around the X-Axis. R(y) = 5+y, r(y)=2 Assuming that part is at least correct. The integral goes from...
  30. S

    MHB Shell Method Example: Finding Volume Around Axes and a Line

    I don't need the answers or the problems worked out I'm asking something more basic. This is just an example problem. y=\sqrt(x),y=0, x=3 a) Around the x-axis R(x)=\sqrt{x}, r(x)=0 I understand the R to be the value fathers from the x-axis, and the r value to be the closer one to the...
  31. F

    Mesh (Loop Current) Method: tightening-up my recipe

    I'm an intro calc-based physics instructor, and recently uncovered some vagueness, or maybe errors (?), with my recipe. Can you please comment on the following? Question 1: Loop Currents - MY RECIPE: "Determine # of loop currents by connecting each circuit junction once, and only once, to a...
  32. T

    Weird shell method problem to find volume

    Y=x^(2/3) and y=x^2 rotated about the x=4. First I equate the equations giving me x=0,-1,1. The problem is I have exactly 2 graphs that are symmetric in respect to the y axis. N I have not encountered a problem in stewart dealing with this. I know that the volume on the right side of the...
  33. W

    How Can Newton-Raphson Method Solve These Complex Nonlinear Equations?

    The three non-linear equations are given by \begin{equation} c[(6.7 * 10^8) + (1.2 * 10^8)s+(1-q)(2.6*10^8)]-0.00114532=0 \end{equation} \begin{equation} s[2.001 *c + 835(1-q)]-2.001*c =0 \end{equation} \begin{equation} q[2.73 + (5.98*10^{10})c]-(5.98 *10^{10})c =0 \end{equation} Using...
  34. R

    MHB How to Solve Non-Linear Equations of 3 Variables Using Newton-Raphson Method?

    The three non-linear equations are given by \begin{equation} c[(6.7 * 10^8) + (1.2 * 10^8)s+(1-q)(2.6*10^8)]-0.00114532=0 \end{equation} \begin{equation} s[2.001 *c + 835(1-q)]-2.001*c =0 \end{equation} \begin{equation} q[2.73 + (5.98*10^{10})c]-(5.98 *10^{10})c =0 \end{equation} Using the...
  35. M

    Simplify Derivative of log(x^2 + y^2) - z^3

    Homework Statement Simplify ##d(log(x^2 + y^2) − z^3)## Homework Equations the derivative? The Attempt at a Solution The instruction says to simplify. In a similar problem I ended up using the d(a(b-c))= da d(b-c). I am not sure how to deal with the log and only found formulas...
  36. N

    The Lagrange Mesh Method: An Overview

    What is the Lagrange Mesh method?
  37. P

    Why is f(y,t+h) Equal to y(t+2) in Implicit Euler Method?

    Hey I don't understand this backward euler solution, in particular why the f(y,t+h) is equal to y(t+2)
  38. S

    MHB Finding an Expression for Y in a Linear Multistep Method

    consider the following LMM $$y_n-\frac{3}{2}y_{n-1}+\frac{1}{2}y_{n-2}=h(\frac{1}{2}f_n+\frac{1}{4}f_{n-1}-\frac{1}{4}f_{n-2})$$ which is applied to the initial value problem $$y'(t)=y(t),0\leq{t}\leq{1}\\ and\\ y(0)=1$$ How do i find an expression for $$y_n$$, if the starting values are...
  39. F

    Estimate Microbial Number: MPN Method for CFU

    Hi, I just want to know should I only use counts in tube3 to estimate microbial number, or the average of tube2 and tube3 estimation. Thank you!
  40. R

    MHB Boundary integral method to solve poisson equation

    Suggest how to solve Poisson equation \begin{equation} σ ∇^2 V = - I δ(x-x_s) δ(y-y_s) δ(z-z_s) \nonumber \end{equation} by using the boundary integration method to calculate the potential $V(r,z)$ with the help of changing the Poisson equation into cylindrical polar co ordinates? Where V is...
  41. A

    The motivation of k.p method and envelope function method?

    There are various kinds of approximation methods in band theory. In my opinion, Bloch theorem implies the existence of energy band. From nearly-free electron approximation or tight binding method, we can calculate the energy band. They can tell us the information of band gap and band width...
  42. M

    Constructing Bending Moment Diagram for Member 1-5 Using Stiffness Matrix Method

    This problem has a lot of calculations from the beginning so i have skipped to the part i am stuck with and tried to include relevant information, apologies if i have missed anything. Assume all working is correct as i was given the answers. After carrying out the stiffness matrix method I am...
  43. P

    Example of the method of characteristics

    Homework Statement Hi,guys I have a example, i understand almost everything but i have problems understanding some steps. Example: 2u't+3u'x=0,x\inR,t>0,u(x,0)=sin(x),u=u(x,y) The Attempt at a Solution I rewrite the example (1)2u't+3u'x=u's (2)u'tt's+u'xx's=u's From comparing (1)...
  44. T

    Volume Measurement (Dry Method)

    Hi: I have been working in this Project for a while now and I would like to share the results with you. Still needs some improvements; but it appears to be working fine so far. Please let me know your suggestions and ideas. Thanks.
  45. Q

    Radius of the smallest exoplanet detectable with the transit method

    Please help me with this astronomy problem. I am supposed to calculate the smallest planet that is detectable with the transit method, given a signal to noise ratio and a star's radius: Suppose the star is seen at its distance D with a signal to noise ratio of S/N = 10^4. This means that in...
  46. N

    Bisection method and multiple roots

    Hello, I have a polynomial of order n and I want to find all it's roots with bisection method. Is it possible? I already wrote an algorithm to find a root and it's works nice for finding one of it's roots, but what about others? Nikola
  47. F

    2nd Order Differential Equation with Improved Euler Method (Heun's)

    Homework Statement I would like to solve a 2nd Order Differential Equation using the Improved Euler Method. The 2nd ODE is a Mass-Spring-Damper equation. I tried coming up with an solution for the Improved Euler Method, but not entirely sure. Can you help me and have a look if this is correct...
  48. J

    Karatsuba Method Homework: Check 3(r-1) Multiplications in F

    Homework Statement For polynomials f(x),g(x) of degree d = 2(r−1)−1, check that multiplying f(x) and g(x) by the Karatsuba method requires 3(r-1) multiplications in the field F. Homework Equations You can can more clearly see problem on page 383 #10...
  49. B

    MHB Do you have a diferent method to solve this Integral?

    Integral[(dx/(ex+1)] Here’s my method: If x = -Ln(u) Then dx = -du/u; ex = 1/u; u = e-x; Substituting in the integral we get: Integral[(-du/u)/((1/u)+1)] = -Integral[du/(1+u)] Solving the integer in terms of u: -Ln|1+u|+C Substituting x in the result: -Ln|1+e-x|+C Sorry that i didn't use the...
  50. S

    MHB Energy Method: Prove True Statements

    how can i use an energy method to show that the following is true
Back
Top