Consider the RDDE's initial value problemwhere a, b and τ are arbitrary real constants, and τ＞ 0, φ(θ) is a given initial function.In this paper, we find series expansions of the accurate solution of the ini...Consider the RDDE's initial value problemwhere a, b and τ are arbitrary real constants, and τ＞ 0, φ(θ) is a given initial function.In this paper, we find series expansions of the accurate solution of the initial valueproblem (EI).展开更多
Poisson's equation is solved numerically by two direct methods, viz. Block Cyclic Reduction (BCR) method and Fourier Method. Qualitative and quantitative comparison between the numerical solutions obtained by two ...Poisson's equation is solved numerically by two direct methods, viz. Block Cyclic Reduction (BCR) method and Fourier Method. Qualitative and quantitative comparison between the numerical solutions obtained by two methods indicates that BCR method is superior to Fourier method in terms of speed and accuracy. Therefore. BCR method is applied to solve (?)2(?)= ζ and (?)2X= D from observed vorticity and divergent values. Thereafter the rotational and divergent components of the horizontal monsoon wind in the lower troposphere are reconstructed and are com pared with the results obtained by Successive Over-Relaxation (SOR) method as this indirect method is generally in more use for obtaining the streamfunction ((?)) and velocity potential (X) fields in NWP models. It is found that the results of BCR method are more reliable than SOR method.展开更多
We employ fundamental equations of non-homogeneous elasticity and Fourierintegral transformations to obtain the general solutions of the stress function.On thebasis of these points of view and when the forces on the b...We employ fundamental equations of non-homogeneous elasticity and Fourierintegral transformations to obtain the general solutions of the stress function.On thebasis of these points of view and when the forces on the boundary are arbityary for nonhomogeneous half-plane problems with the Young’s modulus E(x)-E_0θxp[βx].accurate solutions are obtained At last with the degeneracy it is obtained that thefamous Boussnesq solution and this method is successful.展开更多
In this paper,an implicit finite difference scheme is presented to solve one dimensional unsteady singularly perturbed Burger-Huxley equation.The quadratically convergent quasilinearization technique is used to linear...In this paper,an implicit finite difference scheme is presented to solve one dimensional unsteady singularly perturbed Burger-Huxley equation.The quadratically convergent quasilinearization technique is used to linearize the nonlinear term of the equation.The innovative significance of this paper is the procedure to consider initial guesses in order to start the quasilinearization technique.This basic initial guessing causes to produce a more accurate solutions with the small iteration number for the problem under consideration.The derivatives are replaced by finite difference approximation,then we obtain the two-level time direction and the three-term recurrence relation in the spatial direction.The convergence analysis of the proposed method has been established.Numerical experiments were conducted to support the theoretical results.Further,the result shows that the proposed method gives a more accurate solution with a higher rate of convergence than some existing methods.展开更多
文摘Consider the RDDE's initial value problemwhere a, b and τ are arbitrary real constants, and τ＞ 0, φ(θ) is a given initial function.In this paper, we find series expansions of the accurate solution of the initial valueproblem (EI).
文摘Poisson's equation is solved numerically by two direct methods, viz. Block Cyclic Reduction (BCR) method and Fourier Method. Qualitative and quantitative comparison between the numerical solutions obtained by two methods indicates that BCR method is superior to Fourier method in terms of speed and accuracy. Therefore. BCR method is applied to solve (?)2(?)= ζ and (?)2X= D from observed vorticity and divergent values. Thereafter the rotational and divergent components of the horizontal monsoon wind in the lower troposphere are reconstructed and are com pared with the results obtained by Successive Over-Relaxation (SOR) method as this indirect method is generally in more use for obtaining the streamfunction ((?)) and velocity potential (X) fields in NWP models. It is found that the results of BCR method are more reliable than SOR method.
文摘We employ fundamental equations of non-homogeneous elasticity and Fourierintegral transformations to obtain the general solutions of the stress function.On thebasis of these points of view and when the forces on the boundary are arbityary for nonhomogeneous half-plane problems with the Young’s modulus E(x)-E_0θxp[βx].accurate solutions are obtained At last with the degeneracy it is obtained that thefamous Boussnesq solution and this method is successful.
文摘In this paper,an implicit finite difference scheme is presented to solve one dimensional unsteady singularly perturbed Burger-Huxley equation.The quadratically convergent quasilinearization technique is used to linearize the nonlinear term of the equation.The innovative significance of this paper is the procedure to consider initial guesses in order to start the quasilinearization technique.This basic initial guessing causes to produce a more accurate solutions with the small iteration number for the problem under consideration.The derivatives are replaced by finite difference approximation,then we obtain the two-level time direction and the three-term recurrence relation in the spatial direction.The convergence analysis of the proposed method has been established.Numerical experiments were conducted to support the theoretical results.Further,the result shows that the proposed method gives a more accurate solution with a higher rate of convergence than some existing methods.
