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. Anukriti C.

    Theory behind long division method

    our maths teacher asked us that we all use the long division method to find square roots or cube roots. The question is, why do we do it that way, i.e. taking one or two nos. from the starting, doubling the divisor and all the steps(i guess everyone knows that). can anyone please help me and...
  2. Jehannum

    I need a method of estimating the volume of a gas container

    In the gas industry you often need to know the installation volume of a system, i.e. the amount of gas it contains in the pipework, fitting and meters. If part of the installation is buried or inaccessible this is difficult to estimate. My concept is to estimate installation volume by...
  3. T

    The process of the method of images

    I am really confused that the whole process of the method of image. Suppose I have the + q near the infinite conducting plane which is grounded. My first question is: Is the conducting plane grounded before putting the +q or after putting the +q then grounded? The first question would lead to...
  4. J-dizzal

    Static equilibrium, trusses/section method

    Homework Statement Calculate the forces in members BC, BE, and EF. Solve for each force from an equilibrium equation which contains that force as the only unknown. The forces are positive if in tension, negative if in compression. Homework Equations Sum of forces and moments equal zero. The...
  5. D

    MHB Finding Method of Moments Estimates for Uniform Distribution Parameters

    The problem: Let the five numbers 2,3,5,9,10 come from the uniform distribution on [$\alpha$,$\beta$]. Find the method of moments estimates for $\alpha$ and $\beta$ . I am trying to wrap my head around the idea behind estimates of moments. From what I understand, the first moment is the mean...
  6. E

    Code of the Angular Spectrum Method

    I constructed my code of the Angular Spectrum Method. However, as the distance between the object and the plane of interest increases, the diffraction pattern never disappears; there is still some sort of a diffraction pattern, and I am expecting that it disappears as distance increases. Here...
  7. J-dizzal

    Truss analysis, section method

    Homework Statement Determine the forces in members BC and CG. The forces are positive if in tension, negative if in compression.[/B] Homework Equations ΣF=0 ΣM=0 The Attempt at a Solution I don't know where I am going wrong, My equations include the applied force, since there is only one.
  8. J-dizzal

    Finding Forces in Truss Members Using Method of Sections

    Homework Statement Determine the forces in members BC and CG. The forces are positive if in tension, negative if in compression. Homework Equations ΣF=0 ΣM=0 The Attempt at a Solution im not sure what I am doing wrong here, i think it might be my angle θ? I got 3.66N tension as my answer but...
  9. agent1594

    Prove by method of contradiction

    Homework Statement Using the method of contradiction prove the following. There's no real number x such that |x-2|+|x-3|=1/2 Homework EquationsThe Attempt at a Solution I can see that the least possible value that LHS can take is 1. That is when x=2.5 which is the middle value of 2 and 3...
  10. K

    Method of lines for diffusion equation

    Hello, I am trying to solve the following simple diffusion equation using the method of lines: du/dt=D(du2/dx2)function k=func1() k = [0, 0, 0, 0, 0, 0, 0.4380, 0, 1e5]; %k(9) initial value of the molecules end %k(7) D/dx2 function...
  11. G

    Fortran [Fortran] Filon's method Fourier Transform

    I was told to do a Fourier transform of function by using a Filon's method. I have found the code but I don't know how to include any function to the subroutine. I would be grateful for any example of how to use this code. SUBROUTINE FILONC ( DT, DOM, NMAX, C, CHAT ) C...
  12. I

    Quantum Mechanics - Induction Method

    Let a be a lowering operator and a† be a raising operator. Prove that a((a†)^n) = n (a†)^(n-1) Professor suggested to use induction method with formula: ((a†)(a) + [a,a†]) (a†)^(n-1) But before start applying induction method, I would like to know where the given formula comes from. Someone...
  13. F

    Variation Method: Finding Ground State Energy of 1D Harmonic Oscillator

    Homework Statement Use the variation method to find a approximately value on the ground state energy at the one dimensional harmonic oscillator, H = -ħ^2/(2m) * d^2/dx^2 + 1/2mω^2*x^2 Homework Equations H = -ħ^2/(2m) * d^2/dx^2 + 1/2mω^2*x^2 u(x) = Nexp(-ax^2) <H> = <u|Hu> The Attempt at a...
  14. J

    Can a new desalination method revolutionize access to clean water?

    If sea water is confined in a vacuum of 600 Pascal pressure it will boil and cool until ice forms. There are several problems designing a system using this process. But, when all the engineering is done and a practical system is developed this method will produce potable water from seawater far...
  15. evinda

    MHB Runge-Kutta Method: Showing Order of Accuracy is 2

    Hello! (Wave) The following Runge-Kutta method is given: $$\begin{vmatrix} 0 & 0 & | 0\\ \frac{1}{2} & \frac{1}{2} & | 1 \\ \\ \frac{1}{2} & \frac{1}{2} \end{vmatrix} \\$$ and I want to show that its order of accuracy is $2$. I have tried the following: $$t^{n,1}=t^n \\ t^{n,2}=t^n+...
  16. P

    Questions on Newton's Method: Investigating Convergence & Initial Guesses

    I have three questions regarding Newton's method. https://en.m.wikipedia.org/wiki/Newton-Raphson#Failure_of_the_method_to_converge_to_the_root According to this wikipedia article, "if the first derivative is not well behaved in the neighborhood of a particular root, the method may overshoot, and...
  17. evinda

    MHB Bound of Euler method- nonuniform partition

    Hello! (Wave) Consider a nonuniform partition $a=t_0< t_1< \dots < t_{\nu}=b$ and assume that if $h_n=t^{n+1}-t^n, 0 \leq n \leq N-1 $ is the changeable step, then $\min_{n} h_n > \lambda \max_{n} h_n, \lambda>0$ independent of $n$. Show a bound of the error of Euler method analogous to...
  18. T

    Exploring the Reliability of Euler Method for Orbital Gravity Equations

    Hello everyone, I am curious as to if it is possible to use the Euler Method to solve the gravity differential equations? Would the approximations quickly diverge to inaccurate solutions, or would it stay relatively reliable? Thanks
  19. Foxyquik

    Solar array arrangement calculation method (not due south)

    Hi all, First time post, long time lurker, sorry if this is in the wrong section. I am currently looking at a project that requires a large solar panel array onto a very tight roof area; maximising space is therefore important. Thus, keeping the panels as close together is important. I have a...
  20. Silicon Waffle

    C# C# GetString method from Encoding's Unicode class

    I have a byte array (each character consumes 4 bytes) of size 64 for example, Now I decode it using byte[] bytes={'z','\0','\0','\0','ý','\0','\0','\0','ó','\0','\0','\0','\0','\0','\0','\0','\0','\0','\0','\0','\0','\0','\0','\0','\0','\0','\0','\0','\0','\0',...}; string...
  21. Hepth

    Mathematica [Mathematica] : Method to import C-Code to Expressions

    I have some ugly c-code that was generated from Mathematica in years past with CForm, and looks like : (PolyLog (2,(-1 + t)*pow (-1 + q2h,-1))*pow (q2h - t,-1)*pow (-1 + \ t,-1)* (-8*pow (q2h,3)*pow (t,2) + pow (q2h,4)*(1 + pow (t,2)) - 8*q2h*pow (t,3)*(-3 + 8*t - 5*pow (t,2) +...
  22. thegreengineer

    Substitution method for finding an integral's interval changes

    Look, I was wondering if substituting the variable more than once is valid and hence the definite integral intervals change this way. Consider the following integral (I'm working for finding the volume of a solid of revolution): *\pi \int_{-3}^{5}3^{2}-(\sqrt{\frac{y+3}{2}}+1)^2dy Personally I...
  23. J

    Which sequence acceleration method should I use?

    The sequence that I'm working with is sort of monotonic. It's monotonic most of the time, sometimes there's one number that ruins the trend like 0.0001001 in 0.1, 0.01, 0.001, 0.0001001, 0.0001, ... but those are very rare. Btw, the sequence above is just an example. Is Richardson...
  24. arpon

    Rinkel's modification of Ruchhardt's method

    Homework Statement In Ruchhardt’s method of measuring ##\gamma##, illustrated in Fig. 12.2, a ball of mass ##m## is placed snugly inside a tube (cross-sectional area ##A##) connected to a container of gas (volume ##V##). The pressure ##p## of the gas inside the container is slightly greater...
  25. DEvens

    Learn the Method of Lines: Textbook Resources for Industrial Problem Solving

    Can anybody suggest good resources for me to learn about the method of lines? I have budget to buy textbooks. The boss has received a "request for proposal" from a client with deep pockets. That means they want us to submit a bid for a contract. The client wants us to apply the method of lines...
  26. E

    Angular Spectrum Method and Fourier Transform

    Are the results of the Angular Spectrum Method and the Fourier Transform of a Fresnel Diffraction be different, or the same? Given the same distance between the input and output plane, and the same aperture.
  27. M

    Short method for computing this?

    suppose a side of an equation : 26q+1 , and i want the least positive integer value for q that makes this side of equation divisible by 7, is there any short method to do this ?
  28. SanEng02

    Finding if two sphere's intersect method

    Hi I was just curious if this method of solving whether or not two spheres intersect is a viable method that will give me the correct answer. Say if I am given the two equations of the sphere's is it viable to: Find the centre and radius of each sphere. Find the magnitude of the distance of...
  29. Coffee_

    Convergence of the sequence from Heron's method.

    ##a_1=1## ##a_{n+1}=\frac{1}{2} ( a_{n} + \frac{b}{a_n} )## This should converge to ##\sqrt{b}## but I seem not to be able to prove this. Could someone give me a hint.
  30. Maximtopsecret

    Is the Solution Unique Using the Method of Characteristics?

    Homework Statement : Using the method of characteristics, say if the problem does have a solution; if it does, is the solution unique? [/B] Homework Equations dt=(u^2)dx; The Attempt at a Solution from the formula above follows dt/dx=u^2; then how am I supposed to find and use characteristics?
  31. E

    How to determine inner and outer radii for 'Washer Method'?

    I'm curious if there is a heuristic or method to determine the inner and outer radii as used in the Washer Method, WITHOUT needing to graph anything?
  32. phoenixthoth

    A method for proving something about all sets in ZFC

    I would appreciate any and all feedback regarding this document currently housed in Google docs. Basically, I generalize induction among natural numbers to an extreme in an environment regarding what I call grammatical systems. Then an induction principle is derived from that which holds in...
  33. barryj

    Work in isothermal PV process. Which method is correct?

    Homework Statement Isothermal process![/B] I have a cylinder with base area of 0.01m^2. I have a piston that is 0.1 meters from the bottom giving a volume of 0.001m^3. I have a weight of 1500 Newtons. This gives a pressure of 1.5E5 Pa. Now, I remove 500 Newtons and the piston moves upwards...
  34. N

    MATLAB 3D Finite different method using matlab

    Can anyone show me how to solve the 3D diffusion equation which has been modeled into FDM by using matlab?
  35. B

    Abaqus 6.14 CAE - Imperfection Study

    The title of the project is as follows: A study of the effect of imperfections on the buckling capability of a soda can under axial loading. My group and I are aiming to carry out the following: Linear buckling analysis of soda can to gain first 5 eigenvalues Riks buckling analysis with...
  36. O

    Problem With solving the Eigenvalues of Tight Binding Method

    Dear All, this is my first post on this forum and hopefully I can get what I want. . I am trying to build the band structure of graphene using the tight-binding method based on slater-koster correction. I use a special code to construct both Hamiltonian and overlapping matrix. I have seen when...
  37. K

    Cable rotations formulae or method

    Hello, and thank you for your time. I observed a wire vibrating is good at blocking things trying to pass through their area. for example a rope spinning around can stop a tennis ball thrown through that area. obviously the speed of the rope allows it to "protect" an larger area than its gauge...
  38. B

    Method of Frobenius and indicial equations

    Homework Statement Hello all, I have a quick question, I'm solving a d.e using the Frobenius method and I have the indicial equation: C1(2r-1)(r-1)+C2x(r)(2r+1)=0 Where c1 and c2 are arbitrary constants not equal to zero. Homework EquationsThe Attempt at a Solution My question is, what are...
  39. A

    Euler's Method and Planetary Motion

    Homework Statement Hi there, I wish to use Newton's Laws in conjunction with Euler's Method to model the motion of a planet around a star.Homework Equations 2nd Law F = m*a Law of Universal Gravitation F = -G*M1*M2/r^2 The Attempt at a Solution [/B] First I combined the two laws above...
  40. ranju

    Pole Changing Method: Understanding the Confusion

    I was going through pole changing methods , when I was studying this given figure , I am quite confused in it.. in the text a1a1' & a2a2' are considered as 2 separate coils & it is assumed that both coils are carrying clockwise current , then what that "dot" & "cross" denoting?? Is it the...
  41. T

    Biot-Savart Law method problem

    Homework Statement Homework Equations dB = (μI/4π)(dLsinθ/r^2) The Attempt at a Solution the flat edges of the loop will not contribute to the magnetic field because sinθ = . Only the curved outer loop with radius I will call r2 and length L2 and inner loop with radius r1 and length L1...
  42. evinda

    MHB What is the solution for the given problem using the method of characteristics?

    Hello! (Wave) I want to find the solution of the problem $$(t+u(x,t))u_x(x,t)+tu_t(x,t)=x-t, x \in \mathbb{R}, t>1,$$ $$u(x,1)=1+x$$ using the method of characteristics. That's what I have tried: $$(x(0),t(0))=(x_0,1)$$We are looking for a curve $(x(s),y(s)), s \in \mathbb{R}$ such that...
  43. C

    Armstrong's Modulation Method vs Wideband FM

    Hey guys, quick question. Is the modulation scheme described here (Armstrong's Phase Modulation) simply wide band FM? This Wikipedia article lists the following patent for Ed Armstrong for "Armstrong's Phase Method" and "Wideband FM" 1933 Patent: http://www.google.com/patents/US1941068
  44. P

    What is difference between vortex panel method and source me

    kindly help me with a detailed explanation?
  45. D

    LaPlace transform method to find the equation of motion

    < Mentor Note -- thread moved to HH from the technical math forums, so no HH Template is shown > So this is the problem Here is the question: A 32lb weight strecthes a spring 2ft.The weight is released from rest at the equilibrium position. beginning at t=0, a force equal to f(t)= sint acts on...
  46. S

    Ziegler nichols method (PID control)

    hello there, i just want to ask some questions related to PID controller. currently, i have run zumo robot to detect line by using PID controller approach ziegler nichols method..however, by testing P,PI, and PID, P gives the most accurate when zumo follows the line..which is better actually? P...
  47. gfd43tg

    Ponchon-Savarit Method: Isolating Stages for Separations

    Hello, I am wondering what the purpose of the Ponchon Savarit method is for determining the theoretical number of stages using an enthalpy-concentration diagram. From what I am seeing, the method requires using a xy diagram with the equilibrium curve. Isn't it superfluous to use the H-x diagram...
  48. K

    Computing an integral -- any method

    Hi, I have been trying to find an integral ## \int_{-\infty}^{+\infty} \frac{ e^{-\sqrt{(x^2 + 1)}}}{(x^2 + 1)^2} dx ##. I initially posted this question in the complex analysis forum since I felt it might be done using contour integration. However now I realize it might not be the best way...
  49. P

    Optimization using Newton's method gradient hessian

    Hello, This is my first post here. So I hope I'm posting in the right place, sorry if not. http://homes.soic.indiana.edu/classes/spring2012/csci/b553-hauserk/Newtons_method.pdf I am trying to solve the following numerical optimization function using Netwon's Method: So, if I have the gradient...
  50. M

    Green's function + method of images

    Hello, I'm trying to understand the application of Green's function to find the potential better. I apologize in advance if I start mixing things up a little. From what I understood and seen, we use this method (Green and method of images) in known symmetries (cylindrical/spherical/planar) and...
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