Abstract
In this paper, a block method with one hybrid point for solving Jerk equations is presented. The hybrid point is chosen to optimize the local truncation errors of the main formulas for the solution and the derivative at the end of the block. Analysis of the method is discussed, and some numerical examples show that the proposed method is efficient and accurate.
Highlights
Open AccessJerk is the rate of acceleration change in physics; that is, the time derivative of acceleration, and as such the second velocity derivative, or the third time position derivative
The Jerk vector is here resolved into tangential-normal and radial-transverse components for planar motion, and the normal component is expressed as an affine differential invariant recognized as the aberrancy
Many authors have studied the numerical solutions of the Jerk equation, harmonic balance approach to periodic solutions is used in [3], in [4] they have written the high-order ordinary differential equation in terms of its differential invariants
Summary
Jerk is the rate of acceleration change in physics; that is, the time derivative of acceleration, and as such the second velocity derivative, or the third time position derivative. Many authors have studied the numerical solutions of the Jerk equation, harmonic balance approach to periodic solutions is used in [3], in [4] they have written the high-order ordinary differential equation in terms of its differential invariants. New algorithm for the numerical solutions of nonlinear third-order differential equations was used jacobi-gauss collocation method in [5], He’s variational iteration method was used in [6] for nonlinear Jerk equations. Modified harmonic balance method was used for nonlinear Jerk equations in [7]. We consider a Jerk equation of the form y′′′ = J ( y, y′, y′′). The current work is motivated by optimizing local truncation errors in order to find a hybrid point in a two-step block method to have the most accurate solution for Jerk Equation (1). We organize this paper as follows: The section illustrates the method derivation, Section 3 presents the analysis of the method involving order four, Section 4 presents the numerical examples showing the productivity of the new technique when it is contrasted with the different strategies proposed in the scientific writing
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
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 callDisclaimer: 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.
