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The purpose of this paper is to propose a hybrid optimization approach with high level of solving precision and efficiency for endo-atmospheric ascent trajectory planning of launch vehicles.

Based on the indirect method of optimal control problems, the optimal endo-atmospheric ascent problem with path constraints and final condition constraints is transformed into a Hamiltonian two point boundary value problem (TPBVP). An advanced Gauss pseudo-spectral method is applied to change the Hamiltonian TPBVP into a system of nonlinear algebraic equations, which is solved by a modified Newton method. To guarantee the convergence of the solution, analytical initial guess technology and homotopy technology are also introduced. At last, simulation tests are made.

The hybrid approach for optimal endo-atmospheric ascent trajectory planning has both fast convergence rate and high solution precision. The simulation results indicate that not only the proposed method is feasible but also it is better than the indirect method, which is a most popular approach for solving the optimal endo-atmospheric ascent problem. Given the same degree of solution accuracy, the new method consumes quite less time on the CPU than that of the indirect method.

The new optimization approach has high level of both solution accuracy and efficiency. It can be used in rapid trajectory designing, on-line trajectory planning and closed-loop guidance of launch vehicles. Also, the proposed Gauss pseudo-spectral method in this paper is a new and efficient method for solving general TPBVPs.

The paper provides a new hybrid optimization method for rapid endo-atmospheric ascent trajectory planning of launch vehicles.

The aim of this study is to design a guidance method to generate a smoother and feasible gliding reentry trajectory, a highly constrained problem by formalizing the control variables profile.

A novel accelerated fractional-order particle swarm optimization (FAPSO) method is proposed for velocity updates to design the guidance method for gliding reentry flight vehicles with fixed final energy.

By using the common aero vehicle as a test case for the simulation purpose, it is found that during the initial phase of the longitudinal guidance, there are oscillations in the state parameters which cause to violate the path constraints. For the glide phase of the longitudinal guidance, the path constraints have higher values because of the increase in the atmosphere density.

The violation in the path constraints may compromise the flight vehicle safety, whereas the enforcement assures the flight safety by flying it within the reentry corridor.

An oscillation suppression scheme is proposed by using the FAPSO method during the initial phase of the reentry flight, which smooths the trajectory and enforces the path constraints partially. To enforce the path constraints strictly in the glide phase, ultimately, another scheme by using the FAPSO method is proposed. The simulation results show that the proposed algorithm is efficient to achieve better convergence and accuracy for nominal as well as dispersed conditions.

The purpose of this paper is to study the generalized Couette flow of Eyring-Powell fluid. The paper aims to discuss diverse issues befell for the heat transfer, magnetohydrodynamics and slip.

A hybrid technique based on pseudo-spectral collocation is applied for the solution of nonlinear resulting system.

Viscous fluid results which are yet not available can be taken as a limiting case of presented problem. The results for the case of Hartmann flow can be obtained as a special case when plate velocity is zero, i.e. pressure gradient induced flow. The results for the zero fluid slip and no thermal slip also become special cases of this work, and the results can be recovered by setting, and to zero. These solutions are valid not only for small but also for large values of all emerging parameters.

This model is investigated for the first time, as the authors know.

The low Mach number approximation of the Navier—Stokes equations is of similar nature to the equations for incompressible flow. A major difference, however, is the appearance of a space‐ and time‐varying density that introduces a supplementary non‐linearity. In order to solve these equations with spectral space discretization, an iterative solution method has been constructed and successfully applied in former work to two‐dimensional natural convection and isobaric combustion with one direction of periodicity. For the extension to other geometries efficiency is an important point, and it is therefore desirable to devise a direct method which would have, in the best case, the same stability properties as the iterative method. The present paper discusses in a systematic way different approaches to this aim. It turns out that direct methods avoiding the diffusive time step limit are possible, indeed. Although we focus for discussion and numerical investigation on natural convection flows, the results carry over for other problems such as variable viscosity flows, isobaric combustion, or non‐homogeneous flows.

The purpose of this paper is to propose a numerical scheme based on forward finite difference, quasi-linearisation process and polynomial differential quadrature method to find the numerical solutions of nonlinear Klein-Gordon equation with Dirichlet and Neumann boundary condition.

In first step, time derivative is discretised by forward difference method. Then, quasi-linearisation process is used to tackle the non-linearity in the equation. Finally, fully discretisation by differential quadrature method (DQM) leads to a system of linear equations which is solved by Gauss-elimination method.

The accuracy of the proposed method is demonstrated by several test examples. The numerical results are found to be in good agreement with the exact solutions and the numerical solutions exist in literature. The proposed scheme can be expended for multidimensional problems.

The main advantage of the present scheme is that the scheme gives very accurate and similar results to the exact solutions by choosing less number of grid points. Secondly, the scheme gives better accuracy than (Dehghan and Shokri, 2009; Pekmen and Tezer-Sezgin, 2012) by choosing less number of grid points and big time step length. Also, the scheme can be extended for multidimensional problems.

This paper aims to develop a novel trajectory optimization algorithm which is capable of producing high accuracy optimal solution with superior computational efficiency for the hypersonic entry problem.

A two-stage trajectory optimization framework is constructed by combining a convex-optimization-based algorithm and the pseudospectral-nonlinear programming (NLP) method. With a warm-start strategy, the initial-guess-sensitive issue of the general NLP method is significantly alleviated, and an accurate optimal solution can be obtained rapidly. Specifically, a successive convexification algorithm is developed, and it serves as an initial trajectory generator in the first stage. This algorithm is initial-guess-insensitive and efficient. However, approximation error would be brought by the convexification procedure as the hypersonic entry problem is highly nonlinear. Then, the classic pseudospectral-NLP solver is adopted in the second stage to obtain an accurate solution. Provided with high-quality initial guesses, the NLP solver would converge efficiently.

Numerical experiments show that the overall computation time of the two-stage algorithm is much less than that of the single pseudospectral-NLP algorithm; meanwhile, the solution accuracy is satisfactory.

Due to its high computational efficiency and solution accuracy, the algorithm developed in this paper provides an option for rapid trajectory designing, and it has the potential to evolve into an online algorithm.

The paper provides a novel strategy for rapid hypersonic entry trajectory optimization applications.

The purpose of this paper is to study the steady laminar flow of a pressure driven third‐grade fluid with heat transfer in a horizontal channel. The study serves two purposes: to correct the inaccurate results presented in Siddiqui et al., where the homotopy perturbation method was used, and to demonstrate the computational efficiency and accuracy of the spectral‐homotopy analysis methods (SHAM and MSHAM) in solving problems that arise in fluid mechanics.

Exact and approximate analytical series solutions of the non‐linear equations that govern the flow of a steady laminar flow of a third grade fluid through a horizontal channel are constructed using the homotopy analysis method and two new modifications of this method. These solutions are compared to the full numerical results. A new method for calculating the optimum value of the embedded auxiliary parameter ∼ is proposed.

The “standard” HAM and the two modifications of the HAM (the SHAM and the MSHAM) lead to faster convergence when compared to the homotopy perturbation method. The paper shows that when the same initial approximation is used, the HAM and the SHAM give identical results. Nonetheless, the advantage of the SHAM is that it eliminates the restriction of searching for solutions to the nonlinear equations in terms of prescribed solution forms that conform to the rule of solution expression and the rule of coefficient ergodicity. In addition, an alternative and more efficient implementation of the SHAM (referred to as the MSHAM) converges much faster, and for all parameter values.

The spectral modification of the homotopy analysis method is a new procedure that has been shown to work efficiently for fluid flow problems in bounded domains. It however remains to be generalized and verified for more complicated nonlinear problems.

The spectral‐HAM has already been proposed and implemented by the authors in a recent paper. This paper serves the purpose of verifying and demonstrating the utility of the new spectral modification of the HAM in solving problems that arise in fluid mechanics. The MSHAM is a further modification of the SHAM to speed up converge and to allow for convergence for a much wider range of system parameter values. The utility of these methods has not been tested and verified for systems of nonlinear equations. For this reason as much emphasis has been placed on proving the reliability and validity of the solution techniques as on the physics of the problem.

The purpose of this paper is to study the mixed convection in a nanofluid along an inclined wavy surface embedded in a porous medium.

The complex wavy surface is transformed to a smooth surface by employing a coordinate transformation. Using the similarity transformation, the governing equations are transformed into a set of ordinary differential equations and then lineralized using the successive linearization method. The Chebyshev pseudo spectral method is then used to solve linearized differential equations.

The effects of Brownian motion parameter, thermophoresis parameter, amplitude of the wavy surface, angle of inclination of the wavy surface for aiding and opposing flows on the non-dimensional velocity, temperature, nanoparticle volume fraction, heat and nanoparticle mass transfer rates are studied and presented graphically.

This is the first instance in which mixed convection, inclined wavy surface and nanofluid is employed to model fluid flow.

The purpose of this paper is to study heat and mass transfer in copper-water and silver-water nanofluid flow over stretching sheet placed in saturated porous medium with internal heat generation or absorption. The authors further introduce a new algorithm for solving heat transfer problems in fluid mechanics. The model used for the nanofluid incorporates the nanoparticle volume fraction parameter and a consideration of the chemical reaction effects among other features.

The partial differential equations for heat and mass transfer in copper-water and silver-water nanofluid flow over stretching sheet were transformed into a system of nonlinear ordinary differential equations. Exact solutions for the boundary layer equations were obtained in terms of a confluent hypergeometric series. A novel spectral relaxation method (SRM) is used to obtain numerical approximations of the governing differential equations. The exact solutions are used to test the convergence and accuracy of the SRM.

Results were obtained for the fluid properties as well as the skin friction, and the heat and mass transfer rates. The results are compared with limiting cases from previous studies and they show that the proposed technique is an efficient numerical algorithm with assured convergence that serves as an alternative to numerical methods for solving nonlinear boundary value problems.

A new algorithm is used for the first time in this paper. In addition, new exact solutions for the energy and mass transport equations have been obtained in terms of a confluent hypergeometric series.

The purpose of this paper is to present a stable and efficient numerical technique based on modified trigonometric cubic B-spline functions for solving the time-fractional diffusion equation (TFDE). The TFDE has numerous applications to model many real objects and processes.

The time-fractional derivative is used in the Caputo sense. A modification is made in trigonometric cubic B-spline (TCB) functions for handling the Dirichlet boundary conditions. The modified TCB functions have been used to discretize the space derivatives. The stability of the technique is also discussed.

The obtained results are compared with those reported earlier showing that the present technique gives highly accurate results. The stability analysis shows that the method is unconditionally stable. Furthermore, this technique is efficient and requires less storage.

The current work is novel for solving TFDE. This technique is unconditionally stable and gives better results than existing results (Ford et al., 2011; Sayevand et al., 2016; Ghanbari and Atangana, 2020).