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. Hepth

    A Looking for a method of solution/inversion for x*Tanh[x]

    $$ y == x*Tanh[x]$$ Solve for "x". Does this exist? Even in terms of more complicated functions like Lambert W, or possibly recursive solutions/geometric series/etc. Thanks, if anyone can point me in the right direction!
  2. Eveflutter

    Method of differences for a series

    When using the method of differences on a given series, when do you stop listing the terms? Example question: f(r)= ; r∈N State f(r)-f(r+1) in terms of r and hence determine So skipping until the worked answer gives Great so here I included the n+1th term because I'm guessing since the...
  3. C

    Finding a third method to determine light wavelength

    Homework Statement a) explain why a pattern of bright and dark fringes is visible on a screen when a light is shone through a double slit. b) Use this data to determine the wavelength of light being used to create the interference pattern. Do this three different ways. -The angle to the eighth...
  4. J

    I Determining the accuracy of the Variational Method

    The Variational Method allows us to obtain an upper bound on energy of the ground state (and sometimes excited states). Is there any way of determining an upper bound on the error of the energy obtained by the variational method without an analytic or numerical solution to the problem? i.e. Is...
  5. M

    MHB Find the best function grouping with an iterative method

    Hello to everyone! I'm having a problem, banal in form, but perhaps complex in practical application. Let's suppose we have 300 functions y = f (x) of random trend and we want to group these functions into 10 subgroups (each group consisting of 30 functions). However, this grouping must not be...
  6. H

    Calculate Slope at Center of Simply Supported Beam Using Castigliano's Method

    Homework Statement [/B] I have a simply supported beam of length (L) with a concentrated moment (M) in the center, and end reactions of R1 and R2 I need to find the slope at the center of the beam caused by M, using castiglianos method I have found the moment function to be M = (R1*X) +...
  7. Alexanddros81

    Particle Motion; Graphical Method

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  8. A

    Simplicity as an advantage of a certain method or approach to a problem

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  9. Jayalk97

    Quick question about linearization using the small angle method

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  10. W

    A Intermediate Axis Theorem - Lyapunov's Indirect Method

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  11. CMJ96

    Solving 2D Integrals Using Fortran 95 and the Trapezoidal Method

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  12. phantom lancer

    Method of undetermined coefficients -- Help please

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  13. K

    Method for testing discharge resistors in 3 phase capacitors

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  14. M

    MHB Convergence of iteration method - Relation between norm and eigenvalue

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  15. M

    A Solving an ODE Eigenvalue Problem via the Ritz method

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  16. V

    B Can you prove anything using the Scientific Method?

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  17. yecko

    Method of undetermined coefficients

    Homework Statement y″ − 2y′ − 3y = t 3 e 5t cos(3t) ---equation 1 Yp = (At3 + Bt2 + Ct + D) e 5t cos(3t) + (Et3 + Ft2 + Gt + H) e 5t sin(3t) ---equation 2 Homework Equations If there is any term in common, then the entire complex of product that is the choice for Y must be multiplied by t...
  18. Richie Smash

    Prove RS is parallel to KL using vector method

    Homework Statement Hi I have attached an image which shows OK and OM which are position vectors such that OK=k and OM =m R is the mid point of OK and S is a point on OM such that (vec) OS = 1/3 OM L is the midpoint of RM, using a vector method, prove RS is parallel to KL. Homework...
  19. D

    MHB (Integration) Find volume using disk method when rotated about the X-axis

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  20. Wrichik Basu

    A query in integration using method of substitution

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  21. T

    Finite difference method; finding the 'Stencil'

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  22. F

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  23. G

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  24. R

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  25. lc99

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  26. J

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  27. F

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  28. P

    A The method of finding periodic three-body orbits

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  29. D

    MHB Proper method to calculate damage per second for Role Playing Games

    A friend and I have reached a disagreement, and truly neither of us can come up with the math to prove one of us right or wrong. So I pose the question in here for someone to offer me a proof of which theory is correct. The question is about what is the proper way to calculate damage per...
  30. M

    MHB Approximation of eigenvalue with power method

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  31. Enelafoxa

    Confused about the difference method

    Homework Statement Use the diffence method to sum the series ##\sum_{n=2}^N\frac {2n-1}{2n^2(n-1)^2}## Homework Equations from the textbook by Riley i have ##S_N=\sum_{k=1}^m f(N-k+1)-\sum_{k=1}^m f(1-k)## The Attempt at a Solution I prefer to write it as ##S_N=\sum_{k=1}^m...
  32. M

    Most effective method to self-learn a new mathematical topic and or concept?

    I am quite sure at least some members here have their own particular way to go about learning a new topic or concept. But, does anyone have any advice for self learning something that is completely new or different without the help from classmates or a teacher about? I am self learning math...
  33. quasarLie

    Help with using the Runge-Kutta 4th order method

    Homework Statement I have this equations of motion, I have this equations of motion for a schwarchild black hole, I wish to use the 4th order Runge-Kutta method to solve them for a body falling to the black hole from a distance r0 and with L = 0. My problem is I am struggling to apply this...
  34. Mzzed

    I Method for solving gradient of a vector

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  35. J

    Full Bridge Inverter: Got the answer by 1 method, but not by another

    Homework Statement Homework Equations Fourier and then V(output) = 4Vs/(n*3.14) * sin (nwt) where Vs is battery here it's 400V Current = V(output) / X(L). Here X is 2*3.14*100*0.2 The Attempt at a Solution I got V(output) = 4*400/3.14 = 509.55V This is fundamental Peak output voltage. So...
  36. Espoice

    On charge image method over a conducting sphere and its Char

    Hi colleagues, I need your help to figure out some subtle theory problmes I have about this topic. I was thinking about a system composed by a conductive sphere (not grounded) under the effect of a pont charge placed near the sphere. As I know we need two image charges to satisfy the boundary...
  37. F

    A Can Newton's method work with an approximated integral

    I have a system of equations, and one of them is this : ##\int(1-U(y))Dy - H*\int(U(y)-U(y)^2)dy=0## Can Newtons method work if I approximate this integral to be ##\sum_y(1-U(y))-H\sum(U(y)-U(y)^2)=0## y is a set integers in range ##[1,1000]## I have Newtons method working for this same system...
  38. F

    I Please suggest whether I should use delta or dx method.

    I previously made a derivation of Neumann potential. It can be found in the pdf file below. I originally made it in the ##dx## method. It involved equations like ##dm=I dS##. My maths teacher told that such an expression has no meaning, at least in elementary calculus. However I argued that my...
  39. axer

    Chemistry AvLaw - Which is the correct method of finding moles of gases?

    Homework Statement Based on your understanding of Avogadro's law. 1000 L steel storage tank contains 88.5 kg of methane gas, CH4. Calculate no. of moles. The Attempt at a Solution one method= no. of moles=mass/molar mass. no. of moles= 88500/16.04= 5517.4 moles.other method= 1 mol= 22.4 liter...
  40. Hi Im Paul

    Python What's wrong with my bisection method code?

    Hello, I am assigned to write a code using bisection method (aka binary search method) The equation is 10sin(x) - x^3 - N where N = 1,2,3,4,5,6,7 My code is from math import sin def neg(a, b): return a*b> 0 def bisectx(funcx, lowx, highx,n): assert not neg(funcx(lowx,n), funcx(highx,n))...
  41. K

    A Are String Theory physicists violating the Scientific Method

    The Scientific Method says that if a theory disagrees with observations, it has been falsified (according to Karl Popper). String theory predicts that spacetime is 10-D, but it is observed to be 4-D. This is a wrong prediction by the theory. So string theory is falsified. String theorists then...
  42. S

    How Can We Determine the Operational State of a Bulb Without Using an LDR?

    What methods other than Light Dependent Resistor incorporation are there to determine the 'bulb state'? I'm guessing it's going to include the use of another type of optoelectric component? Thanks
  43. C

    Mass Spectra -- determining the method of ionization

    Is there a way to look at mass spectra and determine the method of ionization? I.e., whether it's electrospray, FAB, MALDI, etc.
  44. E

    Curvilinear coordinate adaptive method in COMSOL

    Hello everyone, In the COMSOL v5.1 doc i haven't found the mathematical description on how does the automatic geometry analysis or the curvilinear coordinates adaptive method (it is mentioned that they are similar) works. It would be convenient to have an idea about how does the Ecoil vector...
  45. L

    A Integral equations -- Picard method of succesive approximation

    Equation \varphi(x)=x+1-\int^{x}_0 \varphi(y)dy If I start from ##\varphi_0(x)=1## or ##\varphi_0(x)=x+1## I will get solution of this equation using Picard method in following way \varphi_1(x)=x+1-\int^{x}_0 \varphi_0(y)dy \varphi_2(x)=x+1-\int^{x}_0 \varphi_1(y)dy \varphi_3(x)=x+1-\int^{x}_0...
  46. B

    Can ##a_1## and ##a_2## be zero in the Frobenius' method solution for this DE?

    Homework Statement Use Forbenius' method to solve this DE: $$ 5x^2y''+xy'+(x^3-1)y=0$$ Homework Equations Seek power series solution in the form ##y=\sum _{n=0}^{\infty } a_n x^{n+r}##, ##a_0\neq0## The Attempt at a Solution Sub in the ansatz y, get $$ \sum _{n=0}^{\infty...
  47. R

    Intersecting circles using Newton's Method

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  48. D

    C/C++ Question about a specific class method in C++

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  49. E

    Finite Element Method: Linear vs. Quadratic Elements & DOF

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  50. R

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