Related papers: Status of the differential transformation method
Differential temporal difference (TD) methods are value-based reinforcement learning algorithms that have been proposed for infinite-horizon problems. They rely on reward centering, where each reward is centered by the average reward. This…
Power Series Solution method has been used traditionally for to solve Linear Differential Equations, in Ordinary and Partial form. But this method has been limited to this kind of problems. We present the solution of problems of Non Linear…
Value functions arise as a component of algorithms as well as performance metrics in statistics and engineering applications. Computation of the associated Bellman equations is numerically challenging in all but a few special cases. A…
There has recently been considerable interest in using a nonstandard piecewise approximation to formulate fractional order differential equations as difference equations that describe the same dynamical behaviour and are more amenable to a…
A novel template matching algorithm that can incorporate the concept of deformable parts, is presented in this paper. Unlike the deformable part model (DPM) employed in object recognition, the proposed template-matching approach called…
This paper introduces a new functional expansion framework that extends classical ideas beyond the Taylor series. Unlike traditional Taylor expansions based on local polynomial approximations, the proposed approach arises from exact…
Power Series Solution Method has been traditionally used to solve Ordinary and Partial Linear Differential Equations. However, despite their usefulness the application of this method has been limited to this particular kind of equations. In…
In this work we present a power series method for solving ordinary and partial differential equations. To demonstrate our method we solve a system of ordinary differential equations describing the movement of a random walker on a…
In this paper, we present the new approximate solutions of famous coupled Ramani Equation. In order to obtain the solution, we use the semi-analytic methods differential transform method (DTM) and reduced form of DTM called reduced…
Value functions derived from Markov decision processes arise as a central component of algorithms as well as performance metrics in many statistics and engineering applications of machine learning techniques. Computation of the solution to…
There exists a well established differential topological theory of singularities of ordinary differential equations. It has mainly studied scalar equations of low order. We propose an extension of the key concepts to arbitrary systems of…
This paper proposes a novel non-iterative method to solve power system differential algebraic equations (DAEs) using the differential transformation, a mathematical tool that can obtain power series coefficients by transformation rules…
A systematic theory is introduced for calculating the derivatives of quaternion matrix function with respect to quaternion matrix variables. The proposed methodology is equipped with the matrix product rule and chain rule and it is able to…
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…
Most of the engineering and physical systems are generally characterized by differential and difference equations based on their continuous-time and discrete-time dynamics, respectively. Moreover, these dynamical models are analyzed using…
The method of Taylor series expansion is used to develop a numerical solution to the reactor point kinetics equations. It is shown that taking a first order expansion of the neutron density and precursor concentrations at each time step…
The paper sets forth comprehensive basics of Discrete Thermodynamics of Chemical Equilibria (DTD), developed by the author during the last decade and spread over series of publications. Based on the linear equations of irreversible…
Taylor's formula holds significant importance in function representation, such as solving differential difference equations, ordinary differential equations, partial differential equations, and further promotes applications in visual…
Symmetry is a powerful tool for finding analytical solutions to differential equations, both partial and ordinary, via the similarity variables or via the invariance of the equation under group transformations. It is the largest group of…
An efficient finite-difference time-domain (FDTD) algorithm is built to solve the transverse electric 2D Maxwell's equations with inhomogeneous dielectric media where the electric fields are discontinuous across the dielectric interface.…