In this paper, the cubic and quintic diffusion equation under stochastic non homogeneity is solved using Wiener- Hermite expansion and perturbation (WHEP) technique, Homotopy perturbation method (HPM) and Pickard appr...In this paper, the cubic and quintic diffusion equation under stochastic non homogeneity is solved using Wiener- Hermite expansion and perturbation (WHEP) technique, Homotopy perturbation method (HPM) and Pickard approximation technique. The analytic solution of the linear case is obtained using Eigenfunction expansion .The Picard approximation method is used to introduce the first and second order approximate solution for the non linear case. The WHEP technique is also used to obtain approximate solution under different orders and different corrections. The Homotopy perturbation method (HPM) is also used to obtain some approximation orders for mean and variance. Using mathematica-5, the methods of solution are illustrated through figures, comparisons among different methods and some parametric studies.展开更多
This study investigates the flow and heat transfer of dusty Williamson (MHD) Nanofluid flow over a stretching permeable cylinder in a porous medium. Dusty Williamson Nanofluid was considered due to its thermal propert...This study investigates the flow and heat transfer of dusty Williamson (MHD) Nanofluid flow over a stretching permeable cylinder in a porous medium. Dusty Williamson Nanofluid was considered due to its thermal properties and potential benefits of increasing the heat transfer rate. Firstly, partial differential equations are transformed into coupled non-linear ordinary differential equations through a similarity variables transformation. The resulting set of dimensionless equations is solved analytically by using the Homogony Perturbation Method (HPM). The effects of the emerging parameters on the velocity and temperature profiles as well as skin-friction coefficient and Nusselt number are publicized through tables and graphs with appropriate discussions. The present result has been compared with published papers and found to be in agreement. To the best of author’s knowledge, there has been sparse research work in the literature that considers the effect of dust with Williamson Nanofluid and also solving the problem analytically. Therefore to the best of author’s knowledge, this is the first time analytical solution has been established for the problem. The results revealed that the fluid velocity of both the fluid and dust phases decreases as the Williamson parameter increases. Motivated by the above limitations and the gaps in past works, therefore, it is hoped that the present work will assist in providing accurate solutions to many practical problems in science, industry and engineering.展开更多
In this paper, comparison of homotopy perturbation method (HPM) and homotopy perturbation transform method (HPTM) is made, revealing that homotopy perturbation transform method is very fast convergent to the solution ...In this paper, comparison of homotopy perturbation method (HPM) and homotopy perturbation transform method (HPTM) is made, revealing that homotopy perturbation transform method is very fast convergent to the solution of the partial differential equation. For illustration and more explanation of the idea, some examples are provided.展开更多
In this article,the main objective is to employ the homotopy perturbation method(HPM)as an alternative to classical perturbation methods for solving nonlinear equations having periodic coefficients.As a simple example...In this article,the main objective is to employ the homotopy perturbation method(HPM)as an alternative to classical perturbation methods for solving nonlinear equations having periodic coefficients.As a simple example,the nonlinear damping Mathieu equation has been investigated.In this investigation,two nonlinear solvability conditions are imposed.One of them was imposed in the first-order homotopy perturbation and used to study the stability behavior at resonance and non-resonance cases.The next level of the perturbation approaches another solvability condition and is applied to obtain the unknowns become clear in the solution for the firstorder solvability condition.The approach assumed here is so significant for solving many parametric nonlinear equations that arise within the engineering and nonlinear science.展开更多
In this research work, Homotopy perturbation method (HPM) is applied to find the approximate solution of the Van der Pol Differential equation (VDPDE), which is a well-known nonlinear ODE. Firstly, the approximate sol...In this research work, Homotopy perturbation method (HPM) is applied to find the approximate solution of the Van der Pol Differential equation (VDPDE), which is a well-known nonlinear ODE. Firstly, the approximate solution of Van Der Pol equation is developed using Dirichlet boundary conditions. Then a comparison between the present results and previously published results is presented and a good agreement is observed. Finally, HPM method is applied to find the approximate solution of VDPDE with Robin and Neumann boundary conditions.展开更多
In this paper, the time-fractional coupled viscous Burgers' equation(CVBE)and Drinfeld-Sokolov-Wilson equation(DSWE) are solved by the Sawi transform coupled homotopy perturbation method(HPM). The approximate seri...In this paper, the time-fractional coupled viscous Burgers' equation(CVBE)and Drinfeld-Sokolov-Wilson equation(DSWE) are solved by the Sawi transform coupled homotopy perturbation method(HPM). The approximate series solutions to these two equations are obtained. Meanwhile, the absolute error between the approximate solution given in this paper and the exact solution given in the literature is analyzed. By comparison of the graphs of the function when the fractional order α takes different values, the properties of the equations are given as a conclusion.展开更多
首先分析了检波器现有标定方法存在的问题,并且进行了实验研究。研究结果表明信号源输出功率未实时监测和检波器驻波比引起的反射是检波器灵敏度存在差异的主要原因。在此基础上提出了改进后的检波器标定方法,并且实验验证了改进后标定...首先分析了检波器现有标定方法存在的问题,并且进行了实验研究。研究结果表明信号源输出功率未实时监测和检波器驻波比引起的反射是检波器灵敏度存在差异的主要原因。在此基础上提出了改进后的检波器标定方法,并且实验验证了改进后标定方法的正确性。分别采用Agilent信号源和Agilent矢量网络分析仪研究了HPM常用测量器件窄脉冲和连续波下的衰减量差异。研究结果表明:测量器件衰减环节窄脉冲下衰减量可采用矢网连续波测试结果,二者最大差别约0.3 d B。展开更多
基于麦克斯韦方程和电子流体方程构成的完备系,利用时域有限差分法,对高功率微波(high power microwave,HPM)低空水平传输的非线性衰减进行了数值模拟。结果表明,在空气击穿发生的区域里,部分微波能量会被吸收,但仍有大量的能量可继续...基于麦克斯韦方程和电子流体方程构成的完备系,利用时域有限差分法,对高功率微波(high power microwave,HPM)低空水平传输的非线性衰减进行了数值模拟。结果表明,在空气击穿发生的区域里,部分微波能量会被吸收,但仍有大量的能量可继续向前传输;HPM脉冲场强超过击穿阈值愈高时,空气对脉冲能量的吸收愈大。展开更多
文摘In this paper, the cubic and quintic diffusion equation under stochastic non homogeneity is solved using Wiener- Hermite expansion and perturbation (WHEP) technique, Homotopy perturbation method (HPM) and Pickard approximation technique. The analytic solution of the linear case is obtained using Eigenfunction expansion .The Picard approximation method is used to introduce the first and second order approximate solution for the non linear case. The WHEP technique is also used to obtain approximate solution under different orders and different corrections. The Homotopy perturbation method (HPM) is also used to obtain some approximation orders for mean and variance. Using mathematica-5, the methods of solution are illustrated through figures, comparisons among different methods and some parametric studies.
文摘This study investigates the flow and heat transfer of dusty Williamson (MHD) Nanofluid flow over a stretching permeable cylinder in a porous medium. Dusty Williamson Nanofluid was considered due to its thermal properties and potential benefits of increasing the heat transfer rate. Firstly, partial differential equations are transformed into coupled non-linear ordinary differential equations through a similarity variables transformation. The resulting set of dimensionless equations is solved analytically by using the Homogony Perturbation Method (HPM). The effects of the emerging parameters on the velocity and temperature profiles as well as skin-friction coefficient and Nusselt number are publicized through tables and graphs with appropriate discussions. The present result has been compared with published papers and found to be in agreement. To the best of author’s knowledge, there has been sparse research work in the literature that considers the effect of dust with Williamson Nanofluid and also solving the problem analytically. Therefore to the best of author’s knowledge, this is the first time analytical solution has been established for the problem. The results revealed that the fluid velocity of both the fluid and dust phases decreases as the Williamson parameter increases. Motivated by the above limitations and the gaps in past works, therefore, it is hoped that the present work will assist in providing accurate solutions to many practical problems in science, industry and engineering.
文摘In this paper, comparison of homotopy perturbation method (HPM) and homotopy perturbation transform method (HPTM) is made, revealing that homotopy perturbation transform method is very fast convergent to the solution of the partial differential equation. For illustration and more explanation of the idea, some examples are provided.
文摘In this article,the main objective is to employ the homotopy perturbation method(HPM)as an alternative to classical perturbation methods for solving nonlinear equations having periodic coefficients.As a simple example,the nonlinear damping Mathieu equation has been investigated.In this investigation,two nonlinear solvability conditions are imposed.One of them was imposed in the first-order homotopy perturbation and used to study the stability behavior at resonance and non-resonance cases.The next level of the perturbation approaches another solvability condition and is applied to obtain the unknowns become clear in the solution for the firstorder solvability condition.The approach assumed here is so significant for solving many parametric nonlinear equations that arise within the engineering and nonlinear science.
文摘In this research work, Homotopy perturbation method (HPM) is applied to find the approximate solution of the Van der Pol Differential equation (VDPDE), which is a well-known nonlinear ODE. Firstly, the approximate solution of Van Der Pol equation is developed using Dirichlet boundary conditions. Then a comparison between the present results and previously published results is presented and a good agreement is observed. Finally, HPM method is applied to find the approximate solution of VDPDE with Robin and Neumann boundary conditions.
基金Project supported by the National Natural Science Foundation of China (No. 10561151)the Basic Science Research Fund in the Universities Directly Under the Inner Mongolia Autonomous Region(No. JY20220003)the Scientific Research Project of Hetao College of China (No. HYZQ202122)。
文摘In this paper, the time-fractional coupled viscous Burgers' equation(CVBE)and Drinfeld-Sokolov-Wilson equation(DSWE) are solved by the Sawi transform coupled homotopy perturbation method(HPM). The approximate series solutions to these two equations are obtained. Meanwhile, the absolute error between the approximate solution given in this paper and the exact solution given in the literature is analyzed. By comparison of the graphs of the function when the fractional order α takes different values, the properties of the equations are given as a conclusion.
文摘首先分析了检波器现有标定方法存在的问题,并且进行了实验研究。研究结果表明信号源输出功率未实时监测和检波器驻波比引起的反射是检波器灵敏度存在差异的主要原因。在此基础上提出了改进后的检波器标定方法,并且实验验证了改进后标定方法的正确性。分别采用Agilent信号源和Agilent矢量网络分析仪研究了HPM常用测量器件窄脉冲和连续波下的衰减量差异。研究结果表明:测量器件衰减环节窄脉冲下衰减量可采用矢网连续波测试结果,二者最大差别约0.3 d B。
文摘基于麦克斯韦方程和电子流体方程构成的完备系,利用时域有限差分法,对高功率微波(high power microwave,HPM)低空水平传输的非线性衰减进行了数值模拟。结果表明,在空气击穿发生的区域里,部分微波能量会被吸收,但仍有大量的能量可继续向前传输;HPM脉冲场强超过击穿阈值愈高时,空气对脉冲能量的吸收愈大。
