Abstract
The finite difference technique is oldest numerical method to solve differential equations. Like many differential equations, Helmholtz differential equation which is used to describe many physical phenomena, has long been solved using finite difference method. can be described by Helmholtz Differential equations. The solution of the Helmholtz type differential equations is very important. The information that it belongs together because it tells one coherent story just knowing a little bit about finite differences through to how to solve differential equations an especial technique is used, how to implement finite difference method and the tool which is used as generic enough that will immediately be given a whole new differential equation. The analysis of small to moderate sized presented with the help of a few examples. The improved finite difference method is presented with examples, the method is simple, clear, and short the MatLab code is available, the improved finite difference method is suitable and easy to implement, manually as well as computationally.
Highlights
I n The finite difference approximation method [1], [2], changes differential equations, whether an ordinary differential or partial differential equation into, a linear system of equations, and it does not give a symbolic solution
Many problems related to steady state oscillations, and wave scattering [3] is modelled by the Helmholtz equation [4], [5], [6], [7]
The basic philosophy of the finite difference, what would do is in the governing differential equation, we manipulate the governing differential equation directly
Summary
I n The finite difference approximation method [1], [2], changes differential equations, whether an ordinary differential or partial differential equation into, a linear system of equations, and it does not give a symbolic solution. F ′(x1) = rise = f2 − f0 run 2∆x f ′(x3) = rise = f4 − f2 run 2∆x f ′(x4) = rise = f5 − f3 run 2∆x f ′(x5) = rise = f6 − f4 run 2∆x This technique is difficult when considering several points, which is usual practice to get accurate solution of the differential equations in that case above method will be cumbersome, to be incorporated, we need to change strategy; Fig. 2: The derivative of a function goemetricaly presented at any prescribed point. It is important that, finite differences when we are using them when we are deriving them we need to have a good knowledge of the distribution of points from which we are calculating the finite difference and where that finite difference is calculating the derivative or interpolating the function Another way to solve the ODE boundary value problems is the finite difference method, where we can use finite difference formulae at evenly spaced grid points to approximate the differential equations. Different cases are considered with two different types of boundary conditions and different grid sizes to compare the solutions at different grid sizes
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Quaid-e-Awam University Research Journal of Engineering, Science & Technology
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
