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How can I get the correct inverse metric with Physics?
I am looking to do some gravitational perturbations around a generic background spacetime. But before doing that, I wanted to look at just linearized gravity, and make sure all the standard...
View ArticleSimulation on perturbations
Consider a wave y=f(x,t) with amplitude modulation such that it becomes y_new=(1+A)*f(x,t), where A=A(t) is a small perturbation.How can I do the simulation to test the robustness of the system to see...
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New book using Maple, published by SIAM
I am very pleased to announce the publication of my new book written together with Nic Fillion, "Perturbation Methods Using Backward Error", which uses Maple heavily throughout.You can find it atthe...
View ArticleA 2026 Calendar made using Maple
As I have stated "a few times" here on Maple Primes, I've written a new book with Nic Fillion on perturbation methods. The book will be published by SIAM early next year. To help market the book, I...
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How do I use Homotopy Perturbation Method to find an analytical solution for...
Please, I need to use Maple to solve Euler-Bernoulli Beam on Pasternak Foundation using Homotopy Perturbation Method.The governing equation is initial conditions are the boundary condition is The...
View ArticleSolving an ODE perturbation problem.
I have this problem:(x'+x''+epsilon/x)(x'-(x')^3/3!)(x''-(x'')^3/3!)(epsilon/x -(epsilon/x)^3/3!)=1x(0)=epsilon , x'(epsilon)=epsilon+epsilon^{-1}0<epsilon<<1Now I want to try the ansatz:...
View ArticleA book in progress, relying on Jupyter notebooks with Maple
My friend and colleague Nic Fillion and I are writing another book, this one on perturbation methods using backward error analysis (and Maple). We have decided to make the supporting materials...
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Solution of Logistic equation in Perturbation theory
Hi everyone, Please I need your help, if anyone has idea of using Perturbation Theory to Solve the following Logistic Fractional Equation and ploting with iteration....
View ArticleIs there any plot that can show perturbation of eigenvectors
If decimal place is 1 such as 123.1 as input matrix and output matrix is eigenvectoris there a easy way to see changes of eigenvector in graph ?because 3 x 3 matrix has 9 elements and eigenvector each...
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Perturbation with anti-secularity is older than was thought
Dear all,Recently we learned that the idea of "anti-secularity" in perturbation methods was known to Mathieu already by 1868, predating Lindstedt by several years. The Maple worksheet linked below...
View ArticleAnalytical solution of ODE?
Hi, I am tryig to solve ode with the perturbation method but getting an error. can anyone correct my fil and i also want to draw the graph of the involved parameter beta and how can I compare the...
View ArticleWhy the solution is not shown in a complete form?
As you can see in the code, I am trying to print the solution of the ODE using the Homotopy perturbation method for N = 10 ( f[0] till f[10]), but Maple is only printing f[0],f[1], and the rest of the...
View ArticleSimulation on perturbations
Consider a wave y=f(x,t) with amplitude modulation such that it becomes y_new=(1+A)*f(x,t), where A=A(t) is a small perturbation.How can I do the simulation to test the robustness of the system to see...
View ArticleClik here to view.
How do I use Homotopy Perturbation Method to find an analytical solution for...
Please, I need to use Maple to solve Euler-Bernoulli Beam on Pasternak Foundation using Homotopy Perturbation Method.The governing equation is initial conditions are the boundary condition is The...
View ArticleHow expand in perturbation series in maple?
I have the following ODE perturbation problem which I want maple to solve for me:q'(\tau)=f(p(eps*\tau)+eps*q(\tau),r(eps*\tau)+s(\tau))-f(p(eps*\tau,r(eps*\tau)+s(\tau))-f(p(eps*\tau),r(eps*\tau))...
View ArticleIs there any plot that can show perturbation of eigenvectors
If decimal place is 1 such as 123.1 as input matrix and output matrix is eigenvectoris there a easy way to see changes of eigenvector in graph ?because 3 x 3 matrix has 9 elements and eigenvector each...
View Articleasking for training exercise
Dear sir / madam Hi I'm a student of mechanical engineering and looking for some HPM ( homotopy perturbation method) maple codes with the related article to practice more in this field. can I ask you...
View ArticleHow do I use Maple to Solve a Differential Equation in Second-Order...
I am working with the following differential equation:$\frac{d^2z}{dx^2}+z=\frac{\cos 2x}{1+\epsilon z},\:\:\:z(-\pi/4)=z(\pi/4)=0$where modulus of $\epsilon$ is much less than $1$. The task is then...
View Articleperturbation theorie
Hi all, I am having the follwing DE:restart: (diff(z(x), x, x))-z(x) - cos(2*x)/(1+delta*z(x)) = 0:With initial conditions: z(-pi/4)=z(pi/4)=0 and |delta|<<1I showed by hand by using...
View Articlehow to solve by vim or DTM?
hi dears. i cant solve this question by Analytical method such variational itteration method (VIM) or homotopy perturbation method (HPM), homotopy analysis method(HAM) 1)...
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