A New Numerical Approach for the Laminar Boundary Layer Flow and Heat Transfer along a Stretching Cylinder Embedded in a Porous Medium with Variable Thermal Conductivity by S. Shateyi, G. T. Marewo

“…A suitable similarity transformation is employed to transform the partial differential equations corresponding to the momentum and heat equations into nonlinear ordinary differential equations. …”
Get full text

Modelling of vehicle motion control by Narimantas Listopadskis

“…Motion of the vehicle is determined by system of differential equ­ations. Fourth-order Runge–Kutta adaptive method was used for solving of the obtained system of the differential equations. …”
Get full text

Modelling of vehicle motion by Narimantas Listopadskis

“…Motion of the vehicle is determined by system of differential equations. Fourth-order Runge-Kutta adaptive method was used for solving of the obtained systems of the differential equations. …”
Get full text

Derivation of ODEs and Bifurcation Analysis of a Two-DOF Airfoil Subjected to Unsteady Incompressible Flow by H. Alighanbari, S. M. Hashemi

“…The aeroelastic integro-differential equations of motion for the airfoil are reformulated into a system of six first-order autonomous ordinary differential equations. …”
Get full text

Weighted Stepanov-Like Pseudoperiodicity and Applications by Zhinan Xia

“…Furthermore, the existence and uniqueness of the weighted pseudoperiodic solution to fractional integro-differential equations and nonautonomous differential equations are investigated. …”
Get full text

On Random Dynamical Systems Generated by White Noise Time Change of Deterministic Dynamical Systems by Mohamed Hmissi, Farida Mokchaha

“…We prove that the obtained random dynamical systems are solutions of some stochastic differential equations whenever the deterministic dynamical systems are solutions of ordinary differential equations.…”
Get full text

Exact Finite-Difference Schemes for d-Dimensional Linear Stochastic Systems with Constant Coefficients by Peng Jiang, Xiaofeng Ju, Dan Liu, Shaoqun Fan

“…The authors attempt to construct the exact finite-difference schemes for linear stochastic differential equations with constant coefficients. The explicit solutions to Itô and Stratonovich linear stochastic differential equations with constant coefficients are adopted with the view of providing exact finite-difference schemes to solve them. …”
Get full text

Nonlinear Resonance Interaction between Conjugate Circumferential Flexural Modes in Single-Walled Carbon Nanotubes by Matteo Strozzi, Francesco Pellicano

“…The Rayleigh–Ritz method is applied to approximate linear eigenfunctions of the partial differential equations that govern the shell dynamics. An energy approach, based on Lagrange equations and series expansion of the displacements, is considered to reduce the initial partial differential equations to a set of nonlinear ordinary differential equations of motion. …”
Get full text

Similarity Solutions for Flow and Heat Transfer of Non-Newtonian Fluid over a Stretching Surface by Atta Sojoudi, Ali Mazloomi, Suvash C. Saha, Y. T. Gu

“…The nonlinear coupled partial differential equations (PDE) governing the flow and the boundary conditions are converted to a system of ordinary differential equations (ODE) using two-parameter groups. …”
Get full text

Integral Representation of Functions of Bounded Variation by Z. Lipcsey, I. M. Esuabana, J. A. Ugboh, I. O. Isaac

“…With Bainov’s introduction of impulsive differential equations having solutions of bounded variation, this class of functions had eventually entered into the theory of differential equations. …”
Get full text

A New Numerical Procedure for Vibration Analysis of Beam under Impulse and Multiharmonics Piezoelectric Actuators by Yassin Belkourchia, Lahcen Azrar

“…Thanks to this regularization, the resulting differential equations can be directly discretized using the DQM. …”
Get full text

Stochastic control with state constraints via the Fokker–Planck equation. Application to renewable energy plants with batteries by Bermúdez, Alfredo, Padín, Iago

“…For this purpose, advantage is taken from the fact that optimal control problems for stochastic ordinary differential equations (SDE) can be equivalently formulated as optimal control problems for deterministic partial differential equations (PDE), namely, the corresponding Fokker–Planck equation.…”
Get full text

Lie and Riccati Linearization of a Class of Liénard Type Equations by A. G. Johnpillai, C. M. Khalique, F. M. Mahomed

“…The linearizing transformations are used to transform the underlying class of equations to linear third- and second-order ordinary differential equations, respectively. The general solution of this class of equations can then easily be obtained by integrating the linearized equations resulting from both of the linearization approaches. …”
Get full text

A new finite difference algorithm for boundary value problems involving transmission conditions by Semih Çavuşoğlu, Oktay Sh. Mukhtarov

“…The finite difference method (FDM) is used to find an approximate solution to ordinary and partial differential equations of various type using finite difference equations to approximate derivatives. …”
Get full text

Alternative models for cyclic lemming dynamics by Hao Wang, Yang Kuang

“…Many natural population growths and interactions are affected byseasonal changes, suggesting that these natural population dynamicsshould be modeled by nonautonomous differential equations instead ofautonomous differential equations. …”
Get full text

Applications of Karry-Kalim-Adnan Transformation (KKAT) to Mechanics and Electrical Circuits by Karry Iqbal, Muhammad Kalim, Adnan Khan

“…In this paper, we have used the new integral transformation known as Karry-Kalim-Adnan transformation (KKAT) to solve the ordinary linear differential equations as well as partial differential equations. …”
Get full text

Fractional-View Analysis of Space-Time Fractional Fokker-Planck Equations within Caputo Operator by Saleh Alshammari, Naveed Iqbal, Mohammad Yar

“…The convergent series form solution demonstrates the method’s efficiency in resolving several types of fractional differential equations. Compared to other methods of finding approximate and exact solutions for nonlinear partial differential equations, this technique is more efficient and time-consuming.…”
Get full text

A Note on Impulsive Fractional Evolution Equations with Nondense Domain by Zufeng Zhang, Bin Liu

“…This paper is concerned with the existence of integral solutions for nondensely defined fractional functional differential equations with impulse effects. Some errors in the existing paper concerned with nondensely defined fractional differential equations are pointed out, and correct formula of integral solutions is established by using integrated semigroup and some probability densities. …”
Get full text

Approximate Solutions of Hybrid Stochastic Pantograph Equations with Levy Jumps by Wei Mao, Xuerong Mao

“…We investigate a class of stochastic pantograph differential equations with Markovian switching and Levy jumps. …”
Get full text

Exponential Fitted Operator Method for Singularly Perturbed Convection-Diffusion Type Problems with Nonlocal Boundary Condition by Habtamu Garoma Debela

“…This paper presents the study of singularly perturbed differential equations of convection-diffusion type with nonlocal boundary condition. …”
Get full text