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.

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  1. W

    Asymptotic Expansion of Integrals Using Laplace's Method

    Consider the integral \begin{equation} I_n(x)=\int^{2}_{1} (log_{e}t) e^{-x(t-1)^{n}}dt \end{equation} Use Laplace's Method to show that \begin{equation} I_n(x) \sim \frac{1}{nx^\frac{2}{n}} \int^{\infty}_{0} \tau^{\frac{2-n}{n}} e^{-\tau} d\tau \end{equation} as x\rightarrow\infty...
  2. R

    MHB How Can Laplace's Method Simplify This Integral?

    Consider the integral \begin{equation} I_n(x)=\int^{2}_{1} (log_{e}t) e^{-x(t-1)^{n}}dt \end{equation} Use Laplace's Method to show that \begin{equation} I_n(x) \sim \frac{1}{nx^\frac{2}{n}} \int^{\infty}_{0} \tau^{\frac{2-n}{n}} e^{-\tau} d\tau \end{equation} as $x\rightarrow\infty$. where...
  3. R

    MHB Laplace's Method (Integration)

    Consider the integral \begin{equation} I(x)=\int^{2}_{0} (1+t) \exp\left(x\cos\left(\frac{\pi(t-1)}{2}\right)\right) dt \end{equation} Use Laplace's Method to show that \begin{equation} I(x) \sim \frac{4\sqrt{2}e^{x}}{\sqrt{\pi x}} \end{equation} as $x\rightarrow\infty$. => I have tried using...
  4. K

    How Do I Compute the Integral Using u-Substitution?

    what method should i use? i tried u = x - 4 du = dx i can't continue. enlighten me please
  5. W

    A predictor-corrector method and stability

    A predictor-corrector method for the approximate solution of y'=f(t,y) uses \begin{equation} y_{n+1}-y_{n}=hf_{n} \tag P \end{equation} as predictor and \begin{equation} y_{n+1}-y_{n}=\frac{h}{2}(f_{n+1}-f_{n}) \tag C \end{equation} IF (P) and (C) are used in PECE mode on the...
  6. R

    MHB A predictor-corrector method and stability

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  7. T

    Rack and pinion, motor selection method

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  8. D

    Hybrid Method for Solving linear equations

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  9. D

    Successive Substitution vs Newton's Method

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  10. E

    MHB Solving Equivalent Expressions Using Subtraction Method

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  11. E

    A problem in sections method in analyzing structure

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  12. I

    Simplex Method, Duality Problem

    Hello everyone, I have the following question: Show without using the simplex method that x1=5/26, x2=5/2, x3=27/26 is an optimal solution to the following LPP. Maximize z=9x1+14x2+7x3 subject to 2x1+x2+3x3<= 6 5x1+4x2+x3<= 12 12x2 <= 5 x1,x2,x3 unrestricted...
  13. R

    MHB Harmonic oscillator and symplectic Euler method

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  14. R

    When determining if a decay is possible, is there a method to use?

    Hi, I'm in the process of revision for upcoming exams, one likely question will give a number of decays (~5) and ask if they are possible. I understand baryon number, lepton number (and parity, isospin, and strangeness) must be conserved, but for example for the following: K+ -> neutral...
  15. Q

    What would be the best method for heating copper tubing via nichrome?

    What would be the best method for heating copper tubing via nichrome wire? Voltage is 10
  16. E

    Four Wave mixing and split step Fourier method

    Hello everyone . I need to ask if I want to get the right units for each parameter to be able to get the right results Can anyone define them properly? Like the gamma the initial power of pump or signal dispersion and non linear factors Thank you
  17. PsychonautQQ

    Differential Equations Method of Undetermined Coefficients

    Homework Statement consider y'' + 2y' - 3y = 1 + xe^x, find the particular solution The Attempt at a Solution so f(x) = 1 + xe^x f'(x) =e^x + xe^x f''(x) = 2e^x + xe^x so it looks like my particular solution is going to have a constant term, an e^x term and an xe^x term, so I can...
  18. S

    Gnuplot: x squared minimization method

    Hello, I am using the x squared minimization method to compute two parametres in a function let's say (A,B) which correspondes to the minimum value of x^2. Now if i want to make a contour plot of A,B (A=x axis and B=y axis) for the values of x^2-x^2_(minimum)=1σ=2.3 what is the proper way...
  19. binbagsss

    Magnetic field calculation. Method of Images/superimposition.

    The question is : A cable of circular cross-section and diameter 2 cm has a long cylindrical hole of diameter 1 mm drilled in it parallel to the cable axis. The distance between the axis of the hole and the cable is 5 mm. If the cable has a uniform steady current density of J=10 5 Am-2...
  20. D

    Solving trusses with the Direct Stiffness Method

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  21. O

    MHB Proving Exponential Decay of Solution u_t w/o Poincaré Inequality

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  22. H

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  23. zthompson47

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  24. E

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  25. L

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  26. J

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  27. F

    Finite element method and applied element method

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  28. Z

    Sign confusion when taking gradient (Newton's Method)

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  29. MarkFL

    MHB Kim's Questions on Babylonian Method for Estimating Square Roots

    Here are the questions: I have posted a link there to this thread so the OP can view my work.
  30. Z

    Sign confusion when taking gradient (Newton's Method)

    I'm watching a lecture on Newton's method with n-dimensions but I am kind of hung up on why the professor did not use the negative sign while taking the first gradient? Is there a rule that explains this or something that I'm forgetting? The rest makes sense but highlighted in red is the part I...
  31. D

    Virtual Work Method on a Truss

    Homework Statement I want to calculate the horizontal deflections at joints A and F (using Virtual Work method taught in Structural Engineering). Cross-Sectional Area (A) and E values are provided in the problem, and the attachment has all relevant dimensions and applied loads.Homework...
  32. V

    Uncertanty in a non-linear regression with least squares method

    Homework Statement Ok, so I'm trying to fit a set of data (21000 points to be exact) to a sine function. Homework Equations Y = A*sin(ωt) The Attempt at a Solution I used NumPy to get the parameters A and ω with the least squares method. So far, so good. However, i appear to...
  33. A

    Numerical method to solve a spring system

    Hello everyone, this is my first thread in this comunity. I explain my problem: I have a triangle mesh http://en.wikipedia.org/wiki/Triangle_mesh where at every vertex coincide a mass element and on every edge I add a spring. I would like simulate a deformation model. My idea derive...
  34. M

    C-G coefficients by matrix method

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  35. rsyed5

    MHB How can the lower rectangle method for area approximation be improved?

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  36. S

    Derivative Method for Error in Kinetic Energy formula

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  37. S

    Intraclass Correlation Coefficient (ICC) the appropriate method?

    Homework Statement I wish to determine whether a SINGLE instrument provides reliable measures (test-retest reliability). This single instrument is not random (it's the only one available), and I will take 10 measurements for each individual that is part of a control group (and then again for...
  38. E

    How Does the Raman Effect Impact SSFM in Nonlinear Fiber Optics?

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  39. T

    Alternative to Von Neumann bias correction method

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  40. F

    Particle Mesh Method - FFT with Green Function

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  41. M

    Method for unique collisions between 2 subdivided ellipses

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  42. A

    Frobenius Method: Solving for General Solution of 4xy'' + 2y' + y = 0 [x7/2]

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  43. H

    How Do You Calculate Total Displacement Using the Component Method?

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  44. Y

    Solve Mass Suspension by Component Method

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  45. polygamma

    MHB Evaluating an Integral: Laplace Transform Method

    The typical way to evaluate $ \displaystyle \int_{0}^{\infty} \frac{\cos mx}{a^{2}+x^{2}} \ dx$ is by contour integration. In a recent thread I evaluated that integral using the Laplace transform. http://mathhelpboards.com/analysis-50/advanced-integration-problem-9129.html#post42551My...
  46. S

    Reactions of a redundant frame structure using Unit Load Method

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  47. Z

    Node-voltage method to find current

    Homework Statement Use the node-voltage method to find i_0 in the figure (Figure 1) if v = 29.0V. Homework Equations G = 1/R \sumG connected to node 1 * v_1 - \sumG between node 1 and 2 * v_2 = Current source into node 1 \sumG connected to node 2 * v_2 - \sumG between node 1...
  48. S

    Forward Euler Method for ODE system

    Homework Statement Solve the following system for 0<t<5 u^\prime = u-e^{-2t} v, u(0) = 1 v^\prime = u+3v, v(0) = -2 using Forward Euler method and implement the numerical scheme into a MATLAB code. Homework Equations Forward Euler : \vec x^(\prime)_{n+1} = \vec F(t,\vec x)...
  49. R

    Simple Probability decoding a message (need clarification about method

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  50. M

    Finite Volume Method & Evaluating Integral at Borders for Two-Phase Flow

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