Abstract
We investigate the generalized partial difference operator and propose a model of it in discrete heat equation in this paper. The diffusion of heat is studied by the application of Newton’s law of cooling in dimensions up to three and several solutions are postulated for the same. Through numerical simulations using MATLAB, solutions are validated and applications are derived.
Highlights
In 1984, Jerzy Popenda [1] introduced the difference operator ∆ defined on α u (k ) as ∆ u (k )= u (k +1) −αu (k )
The difference operator ∆ with variable coefficients defined as k(l)
The above study helps us in making a wise choice of material(γ) for better propagation of heat
Summary
In 1984, Jerzy Popenda [1] introduced the difference operator ∆ defined on α u (k ) as ∆ u (k )= u (k +1) −αu (k ). The difference operator ∆ with variable coefficients defined as k(l) equation k( ). =l ( 1, 2, 3, , n ) ≠ 0 on a real valued function v (k ) : n → is defined as,. The equation involving with at least one i = 0 is called generalized partial difference equation. A linear generalized partial difference equation is of the form ∆ v (k ) = u (k ) , the inverse of generalized partial difference ( ). A function v (k ) : n → satisfying (2) is called a solution of Equation (2). Equation (2) has a numerical solution of the form, m v (k ) − v (k − m =) ∑ u (k − r ),. We form partial difference equation for the heat flow transmission in rod, plate and system and obtain its solution
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 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.
