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. Samama Fahim

    I Schrodinger Equation from Ritz Variational Method

    (This is from W. Greiner Quantum Mechanics, p. 293 from the topic of Ritz Variational Method) 1) Are ##\frac{\delta}{\delta \psi^{*}}## derivatives in equations 11.35a and 11.35b? If this is so, we can differentiate under the integral sign to get ##\int d^3x (\hat{H}\psi)## in equation 11.35a...
  2. Vividly

    I Can you solve a Disk, Washer, Shell method problem without drawing a graph?

    Is there a way to solve a Disk,Washer,Shell method problem without actually creating a graph?
  3. T

    Principle of Virtual Work to the FE method

    (I do understand there are many ways to formulate the FE method, but I wish to understand this one.) I understand that Hamilton's Principle is just that: a principle ( a law the recapitulates the equations of motion) I also understand that the Principle of Virtual Work (PVW) is a reformulation...
  4. Pipsqueakalchemist

    Mechanics of machine force analysis with analytical method

    So I was looking at this example problem in my textbook and I don’t understand how they got -168.1 degrees. The part I’m confused with is the first part of the 2nd picture, there’s a coma in the inverse tan, I don’t know what that means.
  5. bob012345

    I FEM 2D Node Equations: Setting Up & Examples

    I wish to set up the node equations for a 2D heated plate with boundary conditions. I understand how to do this in 1D but have not found a suitable example problem worked out in 2D and examples I have seen are very involved and complex. @pasmith showed me you to set up the 1D problem as follows...
  6. Purpleshinyrock

    Engineering How do I find Vth with the node voltage method?

    Hello. I'am practicing circuit analisis about the norton and thevenin's circuits and I can't seem to manage to get the right thevenin's voltage using the node voltage for a) resolution 1) I did source transformation turning the current source(2A) into a voltage source (10V) applied node voltage...
  7. Dario56

    Derivation of McCabe - Thiele Method

    McCabe - Thiele method is used to find minimum number of separation stages or theoretical plates for a given efficiency of separation in distillation for two - component mixture if components have similar enthalpy of vaporization. If components have similar enthalpy of vaporization ,than on...
  8. U

    Engineering Using method of sections to solve for truss systems

    Taking the moments about points A and C, why is a distance of 3 meters used in Fhc and Fhg? Isn’t it supposed to be 1.5 meters for both? I acknowledge that Fhc and Fhg have x and y components, but were we considering the horizontal or vertical component (or both components) of either Fhc and Fhg...
  9. F

    Change of variable for Jacobian: is there a method?

    Hello, This problem comes just prior to introducing change of variables with Jacobian. Given the following region in the x-y plane, I have to choose (with justification) the correct change of variables associated, for ##u\in [0,2]## and ##v \in [0,1]##. The correct choice here is a), but I do...
  10. bikashdaga

    Static variable in static method - how to use?

    I wanted to declare a local variable inside a static method main(). My code looks like this - class Operator { static int a; public static void input() { Scanner in=new Scanner(System.in); System.out.println("Enter the number:"); a=in.nextInt(); //this is...
  11. VVS2000

    I Finding focal length of the lens using "u-v" method

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  12. drooble122

    Method of detached coefficients division

    -1 -2 3 | 1 2 4 9 -31 15 | -1 -7 5 1 2 -3 7 9 -31 15 7 14 -21 -5 -10 15 5 -10 15The quotient has the coefficients -1, -7, 5. Now here is the problem. I assumed the variables would thus be...
  13. guyvsdcsniper

    Method of Images for a single point charge in a capacitor

    Disclaimer: This is not a repost. The problem wants me to calculate the force of a p.c. , that is isolated by itself (this p.c. is the only charge this problem starts with in this problem) inside a capacitor, a distance h/4 from the bottom plate. This is what I have though of so far but I...
  14. guyvsdcsniper

    Method of images between parallel plate capacitor

    Before I can find the force on q I must balance the charges. This problem starts of with -q and q inside the capacitor. I have added image charges on the opposite side of each plate. Would this work?
  15. H

    A Crank-Nicholson method for spherical diffusion

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  16. H

    I Crank Nicolson method to solve a PDE

    Hello, I wrote a code to solve a non-linear PDE using Canrk nicolson method, but I'm still not able to get a correct final results. can anyone tell me what wrong with it?
  17. M

    Why is this method valid to show function is PSD?

    Hi, I was looking at the following example, and I cannot really understand the justification for why this function is positive semi-definite. Example Problem: We are looking at the function: ## f(x, y) = \frac{x^2}{y}, x \in \mathbb{R} , y > 0 ##. Is this function positive semi-definite...
  18. bob012345

    I FEM Method for the Wave Equation

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  19. Dario56

    I What Exactly is Step Size in Gradient Descent Method?

    Gradient descent is numerical optimization method for finding local/global minimum of function. It is given by following formula: $$ x_{n+1} = x_n - \alpha \nabla f(x_n) $$ There is countless content on internet about this method use in machine learning. However, there is one thing I don't...
  20. mcastillo356

    I Looking for Guarantees that the method of fixed-point iteration will work

    Hi PF Not every function works when we try to compute the root with this method The following theorem guarantees that the method of fixed point iteration will work for a particular class of functions A fixed point theorem Suppose that ##f## is defined on an interval ##I=[a,b]## and...
  21. mcastillo356

    I Error bounds for Newton's Method

    Hi, PF Sometimes it is not easy to find roots of functions. Newton gave a nice clue: the Newton's Method formula: ##x_{n+1}=x_n-\dfrac{f(x_n}{f'(x_n)}##. My concern is, now that I have understood and practiced it, comprehend what I've sketched in the summary. This is all taken from "Calculus...
  22. W

    A Does superdeterminism undermine the scientific method?

    Anton Zeilinger, wrote, " "We always implicitly assume the freedom of the experimentalist... This fundamental assumption is essential to doing science. If this were not true, then, I suggest, it would make no sense at all to ask nature questions in an experiment, since then nature could...
  23. yucheng

    Derivation of Boltzmann Factor via Reservoir Method (canonical ensemble)

    https://scholar.harvard.edu/files/schwartz/files/7-ensembles.pdf https://mcgreevy.physics.ucsd.edu/s12/lecture-notes/chapter06.pdf On page 3 of both the notes above, the author merely claims that $$P \propto \Omega_{\text{reservoir}}$$ But isn't $$P \propto...
  24. karush

    MHB 07 division by doubling method

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  25. A

    Engineering Is my method of solving this correct? Superposition theorem

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  26. K

    I Looking for a creative or quick method for finding roots in GF(p^n)

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  27. Wizard

    A Orthogonality of variations in Faddev-Popov method for path integral

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  28. onomatomanic

    [Philosophy of science] Bias inherent in the Scientific Method itself?

    A very "meta" idea crossed my mind today, and I'd like some feedback. Apologies in advance in case the half-formedness of said idea results in a meandering post. The specific connection I made was that the creation-versus-evolution "debate" could be characterized, at its most basic, as the...
  29. S

    Biology Which method would be wrong to use for gene expression?

    I've been struggling, no matter what I try to do I can't come up with a solution. The answer is in situ, but in my mind it would work perfectly fine. The only thing we would do is just use an RNA probe complementary to the gene we are trying to detect and it should light up the moment the gene...
  30. Dario56

    I Du Nouy Method for Measurement of Surface Tension

    This method calculates surface tension based on force balance acting on the ring placed on the liquid surface: $$ F = G + \gamma L $$ where ##G## is weight of the ring, ##L## is wetted length of the ring which is equal to its circumference, ##F## is outer force of tensiometer acting on the ring...
  31. T

    A Hamilton's Method with Lagrange Equation and Constraint

    Good Morning I am "comfortable" with formulating Hamilton's Principle with a Lagrangian (KE - PE), conducting the calculus of variations and obtaining the Euler Lagrange Equations. Advanced mathematical theory, is beyond me. I also have a minimal understanding of using Lagrange multipliers...
  32. B

    B How long it takes the Earth to fall halfway to the Sun--ellipse method

    There's a classic physics problem that is: If Earth is orbiting the Sun at 1 au from and is suddenly stopped. How long does it take to fall into the Sun (neglecting the size of the Sun/Earth)? I know that a clever way to solve this problem is by using degenerate ellipses and an object...
  33. J

    Using the Frobenius method on a 2D Laplace

  34. G

    Comparing Near-Infrared Spectra: What Stat Method?

    I'd like to compare 2 or more near-infrared spectra. The data consists of measured light intensity in different wavelengths (range 600 nm to 1100 nm). I'm wondering which statistical method would be appropriate? I noticed when searching online that pearson correlation might be inaccurate as...
  35. e2m2a

    A Generalized Diophantine equation and the method of infinite descent

    There is an entry in Wikipedia at this link: https://en.wikipedia.org/wiki/Pythagorean_triple Under elementary properties of primitive Pythagorean triples, general properties,sixth bullet from the bottom of this section, there is this generalized Diophantine equation: x^2p + y^2p = z^2 Where: p...
  36. B

    Can Ansys Workbench Improve CZM Method for Material Fracture Analysis?

  37. M

    Basic coin toss problem to get 1 head, but with a different method

    Hi, I was watching a video where the following formula, for expected value, was presented for a discrete probability distribution which cannot take negative values: E[X] = \sum_{j = 1}^{\infty} P(X \geq j) and I never saw this formula before and am trying to develop an intuition for it. I am...
  38. G

    A Image Method for B-Field Calculation on Iron Plate

    Hello, I am wondering if it is possible to calculate the B-field of a conductor above an iron plate just using the complex image method. To keep it simple let’s consider a 2D calculation, the metal plate is infinitely deep and wide and the conductor is infinitely long and thin. If the metal...
  39. V

    Books that teach classical mechanics through a discourse method

    Books that teaches classical mechanics through a discourse method ie asking interesting questions and answering them maybe a similar one to Understanding Basic Chemistry Through Problem Solving: The Learner's Approach Book by Jeanne Tan and Kim Seng Chan. Not exactly asking numerical questions...
  40. M

    MHB Householder method : Which α do we take?

    Hey! 😊 We have the matrix $A=\begin{pmatrix}1 & 4 & -1 \\ 2 & 2 & 7 \\ 2 & -4 & 7\end{pmatrix}$ and we want to calculate the $QR$ factorisation using the Householder method. First we take the first column of the matrix $a_0=\begin{pmatrix}1 \\ 2 \\ 2\end{pmatrix}$. We have that $\alpha=\pm...
  41. M

    MHB Approximation of eigenvalue with inverse iteration method

    Hey! :giggle: We have the matrix $\begin{pmatrix}2 & 1/2 & 1 \\ 1/2 & 3/2 & 1/2 \\ 1 & 1/2 & 2\end{pmatrix}$. We take as initial approximation of $\lambda_2$ the $1.2$. We want to calculate this value approximately using the inverse iteration (2 steps) using as starting vector...
  42. kyphysics

    Reducing Sunburn Damage: Is the 3-Chunk Method Effective?

    rall)? What I mean is, suppose I were to spend 1 hour total in the sun. If I spent it in "3 chunks" of 20 minutes with 10 minutes between each chunk (in the shade), would that reduce my sunburn damage chances vs. spending the full 1 hour entirely in the sun? I was mowing grass in 90...
  43. Arman777

    Python Complexity of the Steganography Encryption Method

    I have implemented steganography encryption and decryption process, and I wondered if someone could decrypt the message in these conditions; (a) without having the original image (b) having the original image. The encryption starts from the first color code and the first pixel. (c) having the...
  44. Einstein44

    Calculating the volume of a bottle of water using disk method

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  45. S

    I General Method for Mapping an Ellipsoid to Unit Sphere

    I have been working on a problem for a while and my progress has slowed enough I figured I'd try reaching out for some more experience. I am trying to map a point on an ellipsoid to its corresponding point on a sphere of arbitrary size centered at the origin. I would like to be able to shift any...
  46. anorlunda

    Judge gets scientific method better than scientists

    https://reason.com/wp-content/uploads/2021/07/b49101a8-ad23-44dc-9500-ecec551c08b8.pdf This was unexpected. In a 55 page decision from the Superior Court of DC, the judge said the following. The scientist litigator, and his expert witnesses said: It seems to me that the judge gets it, and...
  47. D

    Determine the forces using virtual work(unit force method)

    Summary:: Require to determine the designated forces using principle of virtual work ( unit force method ) I have no idea how to determine the multispan beam using virtual work, if I start to analyse the subsidiary portion BC member, the Yc can be calculated and following by the Ma... it seems...
  48. C

    Maple Boundary finite element method in Maple

    I would like any tips about a Maple ''home made'' program that I received for a project but this program seems to stop before the very end of the code. I want to find de lift of an airfoil with Boundary finites elements method. I have this error at the very end : Error, (in fprintf) number...
  49. T

    Solving a Partial Differential Equation with the Characteristic Method

    dx/dt =1, x(0,s)=0, dy/dt=x, y(0,s) = s, du/dt=(y-1/2x^2)^2, u(0,s)=e^s I did well at the beginning to get x(t,s) =t and y(t,s)=1/2t^2 + s, but got stuck with the du/dt part. You can sub in x=t and y=1/2t^2 +s for x and y to get du/dt = s^2. But that's still three variables, and I can't see...
  50. M

    An accurate method to determine the band gap

    Summary:: What is an accurate method to determine the band gap? What is an accurate method to determine the band gap?
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