n this paper, we apply picard’s iteration method followed by adomian decomposition method to solve a nonlinear singular cauchy problem of euler- poisson- darboux equation. the solution of the problem is much simplified and shorter to arriving at the solution as compared to the technique applied by carroll and showalter (1976)in the solution of singular cauchy problem.

The leapfrog method is popular because of its good stability when solving partial differential equations with oscillatory solutions. “It has the disadvantage that the solution at odd time steps tends to drift farther and farther from the solution for even time steps, so it is common to stop the integration every twenty time steps or so and reinitialize with the first order forward Euler method ...

We consider the symplectic Euler method for Hamiltonian systems with holonomic constraints and its generalizations to a class of overdetermined differential-algebraic equations (ODAEs) which are nonlinear in the algebraic variables. It is shown that a straightforward generalization of the symplectic Euler method is inconsistent. A different non-trivial generalization of the symplectic Euler met...

Abstract. Recent results on convergence of fully discrete approximations combining the Galerkin method with the explicit-implicit Euler scheme are extended to strong convergence under additional monotonicity assumptions. It is shown that these abstract results, formulated in the setting of evolution equations, apply, for example, to the partial differential equation for vibrating membrane with ...

In this paper we study numerical methods for hybrid fuzzy differential equations by an application of the Improved Euler method for fuzzy differential equations. We prove a convergence result and give numerical examples to illustrate the theory.

We use an agent-based modeling software, NetLogo, to simulate fabric drape by applying a modified mass spring system. This model provides an application of harmonic motion to textiles and fashion, fields not typically discussed in the undergraduate differential equations classroom. Euler’s method is coded into the model to solve a system of ordinary differential equations describing the fabric’...

The numerical methods in the current known literature require the stochastic differential equations SDEs driven by Poisson randommeasure satisfying the global Lipschitz condition and the linear growth condition. In this paper, Euler’s method is introduced for SDEs driven by Poisson random measure with non-Lipschitz coefficients which cover more classes of such equations than before. Themain aim...

In this paper, the application of the method of lines (MOL) to the KdV equation was presented. The MOL approach of the KdV equation led to a system of ordinary differential equations. Solution of the system was obtained by applying Euler’s method. In order to show the accuracy of the presented method, two test problem whose exact solutions are known were used. The numerical solutions obtained w...

Relatively little is known about the ability of numerical methods for stochastic differential equations (SDEs) to reproduce almost sure and small-moment stability. Here, we focus on these stability properties in the limit as the timestep tends to zero. Our analysis is motivated by an example of an exponentially almost surely stable nonlinear SDE for which the Euler–Maruyama (EM) method fails to...

We derive a new model for seawater intrusion phenomena in free aquifers. It combines the efficiency of the sharp interface approach with the physical realism of the diffuse interface one. More precisely, a phase field is used as an intermediate variable for including the exchanges between the characteristic layers of the aquifer (salt water, fresh water, unsaturated zone). The threedimensional ...