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the euler-lagrange equation plays an important role in the minimization problems of the calculus of variations. this paper employs the differential transformation method (dtm) for finding the solution of the euler-lagrange equation which arise from problems of calculus of variations. dtm provides an analytical solution in the form of an infinite power series with easily computable components. s...

depth estimation of the top of the bedrock in the sedimentary basins is the main goal in geomagnetic explorations. the depth estimation of this kind of anomalies can be done using different methods, in the cases where the bedrock is magnetized. in this article, we use the standard euler deconvolution method and its results to interpret the magnetic data from the reshm region in semnan province ...

Abstract. This paper is concerned with the numerical approximation of stochastic ordinary differential equations, which satisfy a global monotonicity condition. This condition includes several equations with super-linearly growing drift and diffusion coefficient functions such as the stochastic Ginzburg-Landau equation and the 3/2-volatility model from mathematical finance. Our analysis of the ...

In the first part of this work [4] we have studied the approximation problem of Ε/(Χχ) by Ef(X%), where (Xt) is the solution of a stochastic differential equation, (X?) is defined by the Euler discretization scheme with step ^, and /(·) is a given function, only supposed measurable and bounded; we have proven that the error can be expanded in terms of powers of £, under a nondegeneracy conditio...

which is uniform with respect to λ > 0. Recall that we showed that this stability estimate is preserved by the implicit Euler method. However, the explicit Euler method is only stable provided that ∆t < 2/λ, so its stability is not uniform in λ. One consequence is that it is less efficient to compute with the explicit Euler method over long time intervals. Note that in this example, we also hav...

Abstract. In this paper, a linearized backward Euler method is discussed for the equations of motion arising in the Oldroyd model of viscoelastic fluids. Some new a priori bounds are obtained for the solution under realistically assumed conditions on the data. Further, the exponential decay properties for the exact as well as the discrete solutions are established. Finally, a priori error estim...

We consider the stochastic Allen-Cahn equation perturbed by smooth additive Gaussian noise in a spatial domain with smooth boundary in dimension d ≤ 3, and study the semidiscretization in time of the equation by an implicit Euler method. We show that the method converges pathwise with a rate O(∆tγ) for any γ < 1 2 . We also prove that the scheme converges uniformly in the strong Lp-sense but wi...