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In this paper, we have presented an algorithm to generate various black hole solutions in general relativity and alternative theories of gravity. The algorithm involves few dimensional parameters that are assigned suitable values to specify…
Some differential equations are considered in the context of Synthetic Differential Geometry. Here, this means that not only nilpotent infinitesimals, but also the formation of function spaces, is exploited. In particular, we utilize…
When studying boundary value problems for some partial differential equations arising in applied mathematics, we often have to study the solution of a system of partial differential equations satisfied by hypergeometric functions and find…
In this work we state a Theorem on number theory and apply it to solve some ordinary and partial differential equations.
In the case of a large class of static spherically symmetric black hole solutions in higher order modified gravity models, an expression for the associated energy is proposed and identified as a quantity proportional to the constant of…
Adaptive methods for derivation of analytical and numerical solutions of heat diffusion in one dimensional thin rod have investigated. Comperhensive comparsion analysis based on the homotopy perturbation method (HPM) and finite difference…
The evaporation of black holes into apparently thermal radiation poses a serious conundrum for theoretical physics: at face value, it appears that in the presence of a black hole quantum evolution is non-unitary and destroys information.…
The Lie symmetry method is applied to derive the point symmetries for the N-dimensional fractional heat equation. We find that that the numbers of symmetries and Lie brackets are reduced significantly as compared to the nonfractional order…
We review some recent results obtained for black holes using effective field theory methods applied to quantum gravity, in particular the unique effective action. Black holes are complex thermodynamical objects that not only have a…
Quantum computers can produce a quantum encoding of the solution of a system of differential equations exponentially faster than a classical algorithm can produce an explicit description. However, while high-precision quantum algorithms for…
Numerical relativity became a powerful tool to investigate the dynamics of binary problems with black holes or neutron stars as well as the very structure of General Relativity. Although public numerical relativity codes are available to…
The numerical solution methods for partial differential equation (PDE) solution allow obtaining a discrete field that converges towards the solution if the method is applied to the correct problem. Nevertheless, the numerical methods…
In this work we have considered formal power series and partial differential equations, and their relationship with Coding Theory. We have obtained the nature of solutions for the partial differential equations for Cycle Poisson Case. The…
Many problems in science and engineering can be represented by a set of partial differential equations (PDEs) through mathematical modeling. Mechanism-based computation following PDEs has long been an essential paradigm for studying topics…
Black holes are more than just odd-looking curiosities in gravity theory. They uniquely intertwine the basic principles of General Relativity with those of Quantum Theory. Just by demanding that they nevertheless obey acceptable laws of…
In this paper we introduce and investigate a new kind of functional (including ordinary and evolutionary partial) differential equations. The main goal of this paper is to explore our new philosophy by some examples on functional ODEs and…
Physics-informed neural networks (PINNs) constitute a flexible deep learning approach for solving partial differential equations (PDEs), which model phenomena ranging from heat conduction to quantum mechanical systems. Despite their…
In backward error analysis, an approximate solution to an equation is compared to the exact solution to a nearby modified equation. In numerical ordinary differential equations, the two agree up to any power of the step size. If the…
The purpose of this paper is to study a class of ill-posed differential equations. In some settings, these differential equations exhibit uniqueness but not existence, while in others they exhibit existence but not uniqueness. An example of…
The results of difference sequences theory are applied to analytic function theory and Diophantine equations. As a result we have the equation which connects the $n$-th derivative of a function with the difference sequence for the values of…