The muti-scale method and regular perturbation method are used for solving governed equations of nonlinear thermoelastically coupled vibrations of the plate which are derived in [2,3,4].

This article brings forth the variational perturbation method—the known variational function J=J(y,a) is expanded into a series of the small parameter a by using the regular perturbation method and then turned into the linear function to be solved.

With the permeability modulus assumed to be constant and Pedrosa transformation introduced, the nonlinearity of the governing equation for the pressure becomes weaker and the first-order perturbation solution is obtained for a radial reservoir with infinite boundary condition by use of the regular perturbation method.

Introducing Pedrosa transform to weaken the non-linear item in the percolation diffusion equation when the model is solved, and using the regular perturbation equation to accurately derive the zero-order and first-order solutions of the percolation model, the inflow performance equation is established for the wells of stress-sensitive gas reservoirs with high pressure.

An approximate solution for the complete differential equation is given using a regular perturbation technique.

A regular perturbation approach to the problem of diffusion towards a growing mercury drop electrode

The convergence of the results obtained by this approximate technique is checked by comparing the results with those of exact solutions obtained using a regular perturbation technique.

Analytical expressions for the velocity and the angular velocity fields have been obtained, using the regular perturbation technique.

A solution of the Navier-Stokes equations is obtained by employing a regular perturbation technique.

Using regular perturbation method, a series of asymptotic equations and corresponding boundary condtiions of those problems, in which the geometric forms of the boundary surfaces are characterized by small asymmetry, have been established. For every order of the asymptotic solution, the dimensionality of the problem has been decreased by one. Thus the analytic solutions of some two-dimensional problems may be obtained, and some complex three-dimensional problems can be transformed into two-dimensional...

Using regular perturbation method, a series of asymptotic equations and corresponding boundary condtiions of those problems, in which the geometric forms of the boundary surfaces are characterized by small asymmetry, have been established. For every order of the asymptotic solution, the dimensionality of the problem has been decreased by one. Thus the analytic solutions of some two-dimensional problems may be obtained, and some complex three-dimensional problems can be transformed into two-dimensional problems so that the quantity of numerical computation could be much decreased. At the same time, it is bellieved that a theoritical basis and a method of modification have been given to the usually used "revolution-profile-method".

The Lighthill's technique is applied to the solution of heat conduction in a cylindrical body undergoing solidification. The boundary conditions of the first kind and the third kind are considered. The Ste-number, the ratio of the sensible heat to the latent heat, is chosen as small parameter s. The temperature U, the freezing depth S and the time r are expanted as powers in terms of e. The first order term of r is chosen so that the solution is still applicable as the freezing front approaches the center where...

The Lighthill's technique is applied to the solution of heat conduction in a cylindrical body undergoing solidification. The boundary conditions of the first kind and the third kind are considered. The Ste-number, the ratio of the sensible heat to the latent heat, is chosen as small parameter s. The temperature U, the freezing depth S and the time r are expanted as powers in terms of e. The first order term of r is chosen so that the solution is still applicable as the freezing front approaches the center where the regular perturbation solution is found to diverge. The correlation of the entire solidification period with Ste-number and Bi-number is given. The solution obtained is compared with both experimental results and numerical results using the enthalpy model, the agreement is reasonable good.

The purpose of this paper is to develop a regular perturbation method for solving the problem of one dimensional elastic/visco-plastic wave propagation in materials of Malvern's type. Firstly, non-dimensionalized linear multiplication coefficient and damping coefficient of dislocation are introduced as two independent small parameters into the perturbation expansion of solution. Thus, the problem of solving the non-linear wave equations is transformed into finding the solution of homogeneous/nonhomoge-neous...

The purpose of this paper is to develop a regular perturbation method for solving the problem of one dimensional elastic/visco-plastic wave propagation in materials of Malvern's type. Firstly, non-dimensionalized linear multiplication coefficient and damping coefficient of dislocation are introduced as two independent small parameters into the perturbation expansion of solution. Thus, the problem of solving the non-linear wave equations is transformed into finding the solution of homogeneous/nonhomoge-neous telegraph equations. Secondly, an analytical zeroth order approximate solution can be obtained by means of Laplace transform or series expansion technique. Then the first order and higher order approximate solutions are derived from the zeroth order approximate solution based on the method of finding the Riemann function.Through the comparison of the first order approximate solution with the numerical solution of the corresponding non-linear governing equations under the boundary condition of constant stress aσ|x=0= const, it is seen that the first order approximate solution is quite good. Lastly, it appears that, from the results given in this paper, the perturbation method is quite powerful in the study of elastic/visco-plastic wave propagation theory.