scholarly journals Solving Ordinary Differential Equations (ODEs) Using Least Square Method Based on Wang Ball Curves

2022 ◽  
Vol 10 (1) ◽  
pp. 74-87
Author(s):  
Abdul Hadi Bhatti ◽  
Sharmila Binti Karim
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Least Square Method ◽  
Least Square

scholarly journals Solving Nonlinear Second Order Delay Eigenvalue Problems by Least Square Method

2020 ◽  
Vol 33 (4) ◽  
pp. 59
Author(s):  
Israa M. Salman ◽  
Eman A. Abdul-Razzaq
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Eigenvalue Problems ◽  
Least Square Method ◽  
Second Order ◽  
Least Square ◽  
Nonlinear Delay

     The aim of this paper is to study the nonlinear delay second order eigenvalue problems which consists of delay ordinary differential equations, in fact one of the expansion methods that is called the least square method which will be developed to solve this kind of problems.

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.

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.

scholarly journals Stability analysis of heat transfer in nanomaterial flow of boundary layer towards a shrinking surface: Hybrid nanofluid versus nanofluid

2021 ◽  
Author(s):  
Aqeel ur Rehman ◽  
Zaheer Abbas
Keyword(s):  
Heat Transfer ◽  
Stability Analysis ◽  
Differential Equations ◽  
Stable Solution ◽  
Mhd Flow ◽  
Least Square Method ◽  
Dual Solutions ◽  
Least Square ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid

Many boundary value problems (BVPs) have dual solutions in some cases containing one stable solution (upper branch) while other unstable (lower branch). In this paper, MHD flow and heat transfer past a shrinking sheet is studied for three distinct fluids: kerosene hybrid nanofluid, kerosene nanofluid, and kerosene nanofluid. The partial differential equations (PDEs) are turned into ordinary differential equations (ODEs) using an appropriate transformation and then dual solutions are obtained analytically by employing the Least Square method (LSM). Moreover, stability analysis is implemented on the time-dependent case by calculating the least eigenvalues using Matlab routine bvp4c. It is noticed that negative eigenvalue is related to unstable solution i.e., it provides initial progress of disturbance and positive eigenvalue is related to stable solution i.e., the disturbance in solution decline initially. The impacts of various parameters, skin friction coefficient, and local Nusselt number for dual solutions are presented graphically. It is also noted that the results obtained for hybrid nanofluids are better than ordinary nanofluids.

scholarly journals Calculation of ICG kinetics by two simultaneous differential equations and non-linear least square method.

Kanzo ◽  
1988 ◽  
Vol 29 (10) ◽  
pp. 1368-1373
Author(s):  
Yutaka SAGAWA ◽  
Toshiko YOSHIKATA ◽  
Nagaki SHIMADA ◽  
Motonobu SUGIMOTO
Keyword(s):  
Differential Equations ◽  
Least Square Method ◽  
Least Square ◽  
Non Linear ◽  
Linear Least Square

scholarly journals Least Square Homotopy Perturbation Method for Ordinary Differential Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Mubashir Qayyum ◽  
Imbsat Oscar
Keyword(s):  
Differential Equations ◽  
Perturbation Method ◽  
Ordinary Differential Equations ◽  
Homotopy Perturbation Method ◽  
Least Square ◽  
Literature Analysis ◽  
Science And Engineering ◽  
Homotopy Perturbation ◽  
Seventh Order ◽  
Linear And Nonlinear

In this study, a new modification of the homotopy perturbation method (HPM) is introduced for various order boundary value problems (BVPs). In this modification, HPM is hybrid with least square optimizer and named as the least square homotopy perturbation method (LSHPM). The proposed scheme is tested against various linear and nonlinear BVPs (second to seventh order DEs). Validity of the obtained solutions is confirmed by finding absolute errors. To analyze the efficiency of the proposed scheme, tested problems have also been solved through HPM and results are compared with LSHPM. Furthermore, obtained results are also compared with other numerical schemes available in literature. Analysis reveals that LSHPM is a consistent and effective scheme which can be used for more complex BVPs in science and engineering.

Identification and Defect Detection of Continuous Dynamic Systems

2006 ◽  
Author(s):  
A. Siami ◽  
M. Farid
Keyword(s):  
Finite Difference ◽  
Differential Equations ◽  
Defect Detection ◽  
Equations Of Motion ◽  
Continuous System ◽  
Least Square Method ◽  
Least Square ◽  
Continuous Systems ◽  
Algebraic Equations ◽  
Continuous Dynamic

This paper presents a systematic and efficient algorithm using a coupled finite element - finite difference - least square method for identification and defect detection of continuous system using dynamic response of such systems. First the governing partial differential equations of motion of continuous systems such as beams are reduced to a set of ordinary differential equations in time domain using finite elements. Then finite difference method is used to convert these equations into a set of algebraic equations. This set of equations is considered as a set of equality constraints of an optimization problem in which the objective function is the summation of the squares of differences between measured data at specific points and the predicted data obtained by the solution of the governing system of differential of equations. This method has been successfully applied to find mechanical properties of aforementioned systems in an iterative procedure.

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