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.

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  1. Dusty912

    Find the velocity of block a using vector method.

    Homework Statement (Picture attached) Question 1: The system starts at rest. Block a accelerates towards the bottom the the rod. Find the velocity of the block when it is at the bottom of the rod using the "vector method". So this was my midterm question today. I knew how to figure out how...
  2. maistral

    A RK method for heat equation with dependent variables

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  3. FallenApple

    A Does Delta Method work for asymptotic distributions?

    So if I have a logistic regression: ##log (\hat {odds})=\hat{\beta_{0}}+\hat{\beta_{1}}x##. How would I find a confidence interval for x if I am given ##odds=5## This is going in reverse, where if I have the outcome, I try to do inference on the predictor. We know that ##\hat{\vec{\beta}}##...
  4. lawa44

    Direct Stiffness Method for a distributed load

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  5. T

    MHB Solving SIR Model with Euler's Method

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  6. D

    Electrostatics Method of image

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  7. B

    Method of Image charge problem

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  8. P

    Good method for studying boring and mnemonic stuff?

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  9. H

    I Derivative = 0 is always minima? (Linear variational method)

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  10. Const@ntine

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  11. MAGNIBORO

    I What method can be used to solve this pde?

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  12. F

    Find Member Forces of AB and DE: Cut Section Method

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  13. P

    Method for determining the latent heat of oils

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  14. P

    A Genkin-Mednis Method? An extra term -- why?

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  15. Vanessa Avila

    Statics: Method of Joints (Truss)

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  16. F

    How Does FGF sin26.6 Generate Moment About Point D in Truss Analysis?

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  17. C

    Sturm-Liouville Eigenvalue Problem (Variational Method?)

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  18. M

    How Does the Method of Characteristics Solve Nonlinear PDEs?

    Homework Statement $$\frac{\partial u}{\partial t} + x^2 + t+\left(\frac{\partial u}{\partial x}\right)^2 = 0\\ u(x,0)=0$$ Homework Equations $$ \dot{x} = 2 u_x ;\,\,t=0,\,\,x=\xi\\ \dot{u}=2(u_x)^2+u_t ;\,\,t=0,\,\,u=0\\ \dot{u_x}=-2x ;\,\,t=0,\,\,p=0\\...
  19. S

    Find Vx using node voltage method

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  20. Y

    Is the scientific method in physics substantially different?

    Hi, I have two degrees. A BA in physics and a master's in computer science. I've taken more than 30 hours in upper level biology courses and a decent number of hours in mid level chemistry. One thing that I can attest to is that all of the disciplines have a different feel to their respective...
  21. ramzerimar

    Is BEM a More Efficient Alternative to FEA in Computational Science?

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  22. Riverbirdy

    Finite difference Method of Wave Equation

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  23. Bassa

    "Shooting Method" for simulating a Particle in an Infinite Square Well

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  24. C

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  25. Delta31415

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  26. M

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  27. karush

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  28. L

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  29. R

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  30. T

    A Scientific method to calculate the time limits of a task

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  31. Jovy

    Shell Method: Find Vol. of Solid Rotated Around x-Axis

    Homework Statement Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the x-axis. $$y=\frac 1 x$$ Homework Equations $$Volume=2\pi\int_a^b p(y)h(y)dy$$ The Attempt at a Solution [/B] I see that there...
  32. karush

    MHB 242t.9.1.15 Use Euler's method to calculate the first three approximations

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  33. H

    Method Of Loading Carbon Molecular Sieve To Psa Tank

    Dear all I want to loading about 14 ton of CMS (Carbon Molecular Sieve) into a PSA Nitrogen Producer tank. The tank is 5 meter tall with 2 m in diameter. What is the best, simplest and fastest method to load the pellet of CMS into that big tank? I consider this mortar screw pump and connect it...
  34. karush

    MHB 9.1.14 Use Euler's method to calculate

    $\tiny{9.1.14}$ $\textsf{Use Euler's method to calculate the first 3 approximations to the given initial value problem for the specified increment size.}\\$ $\textsf{ Calculate the exact solution.}$ $y'=y^2(5+5x), y(1)=-1, dx=0.2$ $y_1=$ $y_1=0.4$ $y_2=0.6268$ $y_3=1.2694$...
  35. F

    Understanding the Gauss-Seidel Iteration Method: Exploring the Blue Circled Part

    Homework Statement Using the circled formula , here's what i gt (photo3) , , why the author ignore the blue circled part ? Is the author wrong ... If the blue part isn't ignored , i gt this pls refer to the photo 3 which is correct ? The author or me ? Or I'm misunderstanding something ...
  36. B

    Hydrazine Standard Analysis Method

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  37. C

    How to work out thermal diffusivity using Angstrom's method?

    Hi guys, Just looking for some help with the theory on a project I've been set at university. The experiment involved heating a long thin bar from one end with a sinusoidal heat wave. Thermocouples were then placed every 7 cm (4 in total) and temperatures were recorded. The experiment brief...
  38. A

    B First Order Non-Linear ODE (what method to use?)

    Hi, The problem is to solve: dy/dx = −[2x + ln(y)]*(y/x) Attempt: I have tried to see if it is exact, I found it not to be, I can't easily find a function to multiply by to make it exact either (unless I am missing something obvious). It clearly isn't seperable, nor is it homogenous (I know...
  39. F

    SHM question (Is my method correct?)

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  40. evinda

    MHB What is the Method of Four Russians in Dynamic Programming?

    Hello! (Wave)I am reading about the Method of Four Russians from here. We divide the dynamic programming table $D$ into $t$-blocks such that the last row of a $t$ − block is shared with the first row of the $t$ − block below it (if any), and the last column of a $t$ − block is shared with the...
  41. F

    Understanding Stiffness Modification and AA' Beams in Structural Engineering

    Homework Statement I don't understand why the stiffness for span have extension pin stated from original stiffness ... According to online notes , for the far end pin / roller , the k is 3EI / L but not 3EI / 4L , is the notes wrong ? And i don't understand what is AA' beam , can someone...
  42. S

    I Double Blind Method Explained: Particle Physics & LHC

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  43. F

    Is the Stiffness Calculation for Span Ends Incorrect in Online Notes?

    Homework Statement I don't understand why the stiffness for span have extension pin stated from original stiffness ... Homework EquationsThe Attempt at a Solution According to online notes , for the far end pin / roller , the k is 3EI / L but not 3EI ***/ 4*** , is the notes wrong ?
  44. Rocky_Tseng

    Intro Physics Is there a book about how to do research in Physics?

    Is there a book about how to do research in Physics or Physicist's experience? especially in Astrophysics, if not, general physics is also very good. thanks.
  45. F

    Bisection Method Homework: a=-2, b=2, Is b-a=1?

    Homework Statement In the first photo , interval [-2 ,2 ] means a = -2 , b = 2 , am i right ? So , how to show that b-a = 1 ? Homework EquationsThe Attempt at a Solution IMO , b-a = 2+ 2 = 4 for part b , why b - a = -1-(-2) ? Is there anything wrong with this question ?
  46. F

    Slope deflections method analysis of beam

    Homework Statement why we need to consider 2 conditions , the beam curve downwards ( as in 11-3) and beam curve upwards ( as in 11-4) ? What's the difference between 2 cases ? I notice that in both cases , the author assume clockwise as positive here are the 3 consecutive pages of notes...
  47. F

    Slope deflection method for indeterminate beam

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  48. M

    Java Help-Improving runtime complexity of the method

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  49. F

    Method of characteristics please guide me in right direction

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  50. P

    B Guessing trial wave function with variational method

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