Moving least square method for treating nonlinear fourth order integro-differential equations

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
A. Abdollahpoor
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Least Square Method ◽  
Least Square ◽  
Moving Least Square

scholarly journals Numerical Exploration via Least Squares Estimation on Three Dimensional MHD Yield Exhibiting Nanofluid Model with Porous Stretching Boundaries

2021 ◽  
Vol 5 (4) ◽  
pp. 167
Author(s):  
Tamour Zubair ◽  
Muhammad Usman ◽  
Umar Nazir ◽  
Poom Kumam ◽  
Muhammad Sohail
Keyword(s):  
Differential Equations ◽  
Numerical Study ◽  
Nonlinear Partial Differential Equations ◽  
Three Dimensional ◽  
Least Square Method ◽  
Least Square ◽  
Comparison Study ◽  
Nano Fluid ◽  
Complicated Geometry ◽  
Maple Code

The numerical study of a three-dimensional magneto-hydrodynamic (MHD) Casson nano-fluid with porous and stretchy boundaries is the focus of this paper. Radiation impacts are also supposed. A feasible similarity variable may convert a verbalized set of nonlinear “partial” differential equations (PDEs) into a system of nonlinear “ordinary” differential equations (ODEs). To investigate the solutions of the resulting dimensionless model, the least-square method is suggested and extended. Maple code is created for the expanded technique of determining model behaviour. Several simulations were run, and graphs were used to provide a thorough explanation of the important parameters on velocities, skin friction, local Nusselt number, and temperature. The comparison study attests that the suggested method is well-matched, trustworthy, and accurate for investigating the governing model’s answers. This method may be expanded to solve additional physical issues with complicated geometry.

scholarly journals Superresolution of 3-D computational integral imaging based on moving least square method

2014 ◽  
Vol 22 (23) ◽  
pp. 28606 ◽  
Author(s):  
Hyein Kim ◽  
Sukho Lee ◽  
Taekyung Ryu ◽  
Jungho Yoon
Keyword(s):  
Least Square Method ◽  
Least Square ◽  
Integral Imaging ◽  
Moving Least Square ◽  
Computational Integral Imaging

Basic Study on Trend Prediction for Style Design

2008 ◽  
Author(s):  
Shinya Yoshida ◽  
Hideki Aoyama
Keyword(s):  
Product Design ◽  
Least Square Method ◽  
Least Square ◽  
Concept Design ◽  
Trend Prediction ◽  
Basic Study ◽  
Moving Least Square ◽  
And Function ◽  
Eigenvalue And Eigenvector ◽  
Near Future

With diversification of consumer taste, appearance shape together with functionality contributes to the appeal of a product vastly. Concept design and industrial design therefore serve as an important process in product development. These designs are difficult to perform based on theoretical backing, since appearance shape design is a creative activity which depends on a designer’s aesthetic sense strongly. When embodying a product shape, naturally design is determined not only by a designer’s sensitivity but by use and function of a product as well. It is also important to investigate designs desired by consumers, and reflect all of this in the product design. The ability to predict consumer taste trends therefore greatly aids product design. In this research, the prototype models of a product in trend every year were made by multiplying weights according to the number of a product sold in the past to calculate that the rate of exaggeration of prototype models of each year to all whole prototype models. The straight extrapolation of the Spline method was applied to the exaggeration vector, and the technique of predicting shapes preferred by consumers in the near future using that method was proposed. Moreover the eigenspace method was applied to similar product shapes to propose the technique of grasping the features of shape for every year by computing the eigenvalue and eigenvector of the coordinates of the points of the shapes as well as the technique of predicting shapes which consumers will prefer in the near future by using the Linear function of Moving Least Square method.

Least Square Inversed Analysis of Soil Parameter for Foundation with Two-Order Gradient Theoretic Method

2011 ◽  
Vol 243-249 ◽  
pp. 2294-2299 ◽  
Author(s):  
Yao Feng Xie
Keyword(s):  
Differential Equations ◽  
Error Function ◽  
Least Square Method ◽  
Least Square ◽  
Gradient Theory ◽  
Mechanical Theory ◽  
Soil Parameter ◽  
True Value ◽  
Initial Soil ◽  
Calculation Results

Combined with two-order gradient theory, the least square inversed analysis of the soil parameter for the foundation is studied and put forward in detail. After the mechanical theory for the plate on the foundation is introduced, the controlling differential equations of the plate on the foundation which is subjected to vertical loads are deduced. Through utilizing Fourier transformative theory, the corresponding solutions to the plate on the foundation are gained. Linear algebra controlling equations for the plate are achieved which leads to solve the original differential equations more easily. The least square error function for the soil parameter on the plate is established and applied with the two-order gradient method. The inversed steps on the least square error function for the soil parameter are listed. The calculation results verify the conclusions that the soil parameter of the foundation can be efficiently inversed by applying the least square theory. When different initial soil parameter is set, the iterative computations can be convergent to the true value of the soil parameter. And this least square method can also be applied for the problem of inversed analysis of parameters for other foundation models.

Sign in / Sign up

Export Citation Format

Share Document