Papers by Vineet Srivastava
In the frame work of the perturbed restricted three-body problem, the solutions of halo orbits ar... more In the frame work of the perturbed restricted three-body problem, the solutions of halo orbits are developed up to fifth order approximation by using Lindstedt-Poincaré technique. The effect of oblateness of the more massive primary on the size, location and period of halo orbits around L 1 and L 2 are studied by considering the Earth-Moon system. Due to oblateness of the Earth, halo orbits around L 1 and L 2 enlarge and move towards the Moon. Also, the period of halo orbits around L 1 and L 2 decreases. Numerical solution for halo orbits around L 1 and L 2 in the Sun-Earth system is obtained by using the differential correction method for different values of radiation pressure and oblateness. The separation between the orbits obtained using fourth and fifth order Lindstedt-Poincaré method as well as differential correction method is found to be less than the separation between the orbits obtained using third and fourth order Lindstedt-Paincaré as well as differential correction method. This indicates that as the order of the solution increases the separation between consecutive solution decreases leading to more accurate solution.
In this paper, a numerical solution of two dimensional nonlinear coupled viscous Burger equation ... more In this paper, a numerical solution of two dimensional nonlinear coupled viscous Burger equation is discussed with appropriate initial and boundary conditions using the modified cubic B-spline differential quadrature method. In this method, the weighting coefficients are computed using the modified cubic B-spline as a basis function in the differential quadrature method. Thus, the coupled Burger equation is reduced into a system of ordinary differential equations. An optimal five stage and fourth-order strong stability preserving Runge–Kutta scheme is applied for solving the resulting system of ordinary differential equations. The accuracy of the scheme is illustrated by taking two numerical examples. Computed results are compared with the exact solutions and other results available in literature. Obtained numerical result shows that the described method is efficient and reliable scheme for solving two dimensional coupled viscous Burger equation.
The objective of this article is to carry out an approximate analytical solution of the time frac... more The objective of this article is to carry out an approximate analytical solution of the time fractional order Cauchy-reaction diffusion equation by using a semi analytical method referred as the fractional-order reduced differential transform method (FRDTM). The fractional derivative is illustrated in the Caputo sense. The FRDTM is very efficient and effective powerful mathematical tool for solving wide range of real world physical problems by providing an exact or a closed approximate solution of any differential equation arising in engineering and allied sciences. Four test numerical examples are provided to validate and illustrate the efficiency of FRDTM.
In this article, a numerical simulation of two dimensional nonlinear sine-Gordon equation with Ne... more In this article, a numerical simulation of two dimensional nonlinear sine-Gordon equation with Neumann boundary condition is obtained by using a composite scheme referred to as a modified cubic B spline differential quadrature method. The modified cubic B-spline serves as a basis function in the differential quadrature method to compute the weighting coefficients. Thus, the sine-Gordon equation is converted into a system of second order ordinary differential equations (ODEs). We solve the resulting system of ODEs by an optimal five stage and fourth-order strong stability preserving Runge Kutta scheme. Both damped and undamped cases are considered for the numerical simulation with Josephson current density function with value minus one. The computed results are found to be in good agreement with the exact solutions and other numerical results available in literature.
Mars exploring spacecraft “Mars Orbiter Mission” is India’s first interplanetary mission. It is ... more Mars exploring spacecraft “Mars Orbiter Mission” is India’s first interplanetary mission. It is placed in a highly elliptical orbit around the planet Mars with an orbital period of 65 hours and 27 minutes. There was no eclipse on the MOM spacecraft during its interplanetary transfer. During the Martian phase, it started to experience eclipse shadow of Mars from the beginning. In this paper, we discuss several conical shadow eclipse prediction models by accounting the effects of atmospheric dust of Mars considering both spherical and oblate shape of the red planet. A study is performed using the results obtained by different shadow models, Systems Tool Kit (STK), and the actual telemetry data. We notice that effects of the atmospheric dust of Mars cannot be neglected on the MOM spacecraft.
In this paper, our main goal is to present a new approximate series solution of multi-dimensional... more In this paper, our main goal is to present a new approximate series solution of multi-dimensional diffusion (heat like) equation with time-fractional derivative in Caputo form, by using a semi-analytical approach called the fractional-order reduced differential transform method (FRDTM). In addition, four test problems of the multi-dimensional time fractional diffusion equation are considered to confirm the efficiency of FRDTM. The scheme is very efficient, effective, and powerful mathematical tool which provide the exact or a very closed approximate solution of a wide range of real world problems arising in engineering and natural sciences, modeled in terms of partial differential equation.
Acta Astronautica, Feb 7, 2015
A solar eclipse occurs when the Sun, Moon and Earth are aligned in such a way that shadow of the ... more A solar eclipse occurs when the Sun, Moon and Earth are aligned in such a way that shadow of the Moon falls on the Earth. The Moon’s shadow also falls on the Earth orbiting spacecraft. In this case, the alignment of the Sun, Moon, and spacecraft is similar to that of the Sun, Moon, and Earth but this phenomenon is often referred as a lunar eclipse falling on the spacecraft. Lunar eclipse is not as regular in terms of times of occurrence, duration, and depth as the Earth shadow eclipse and number of its occurrence per orbital location per year ranges from zero to four with an average of two per year; a spacecraft may experience two to three lunar eclipses within a twenty-four hour period [2]. These lunar eclipses can cause severe spacecraft operational problems. This paper describes two lunar shadow eclipse prediction models using a projection map approach and a line of intersection method by extending the Earth shadow eclipse models described by Srivastava et al. [10, 11] for the Earth orbiting spacecraft. The attractive feature of both models is that they are much easier to implement. Both mathematical models have been simulated for two Indian low Earth orbiting spacecraft: Oceansat-2, Saral-1, and two geostationary spacecraft: GSAT-10, INSAT- 4CR. Results obtained by the models compare well with lunar shadow model given by Escobal & Robertson [12], and high fidelity commercial software package, Systems Tool Kit (STK) of AGI.
Astronomy and Computing, Oct 16, 2014
In this article, we propose an Earth conical shadow model predicting umbra and penumbra states fo... more In this article, we propose an Earth conical shadow model predicting umbra and penumbra states for the low Earth orbiting satellite considering the spherical shape of the Earth. The model is described using the umbra and penumbra cone geometries of the Earth’s shadow and the geometrical equations of these conical shadow regions into a Sun centered frame. The proposed model is simulated for three polar Sun-synchronous Indian Remote Sensing satellites: Cartosat-2A, Resourcesat-2 and Oceansat-2. The proposed model compares well with the existing spherical Earth conical shadow models such as those given by Vallado (2013), Wertz (2002), Hubaux et al. (2012), Srivastava et al. (2013, 2014). An assessment is carried out of the existing Earth conical shadow models with Systems Tool Kit (STK), a high fidelity commercial software package of Analytic Graphic Inc., and the real time telemetry data.
International Journal of Applied Mathematics and Mechanics, Sep 10, 2014
An explicit-implicit finite difference scheme is proposed for numerical solutions of two dimensi... more An explicit-implicit finite difference scheme is proposed for numerical solutions of two dimensional coupled Burgers' equations. This scheme forms a linear system of algebraic difference equations which is to be solved at each time step. The obtained linear system is solved by direct method. The scheme is implemented to solve three test problems. Comparisons of numerical results with analytical solutions and other available results demonstrate the efficiency and accuracy of the present method for high Reynolds numbers
Egyptian Journal of basic and Applied Sciences
This paper discusses a recently developed semi-analytic technique so called the reduced different... more This paper discusses a recently developed semi-analytic technique so called the reduced differential transform method (RDTM) for solving the (1+n) e dimensional Burgers' equation. The method considers the use of the appropriate initial or boundary conditions and finds the solution without any discretization, transformation, or restrictive assumptions. Four numerical examples are provided in order to validate the efficiency and reliability of the method and furthermore to compare its computational effectiveness with other analytical methods available in the literature.
National Conference on Space Debris Management and Mitigation Techniques, May 21, 2014
"Of-late many debris of defunct satellites and spent stages of rockets in the low earth orbit exi... more "Of-late many debris of defunct satellites and spent stages of rockets in the low earth orbit exist in close conjunction with the operational satellites. It has become essential to monitor space debris and their proximity with the operational satellites very closely and take quick action to carry out orbit maneuvers on
the operational satellites to avoid the collision. This paper describes in-plane orbit maneuvers requirements,
planning and their impact on the spacecraft orbit by considering collision avoidance maneuvers conducted for the six IRS satellites over the last three years. We further emphasis the challenges of scheduling a maneuver to IRS satellites at a very short notice taking into account routine payload operations, on-board and other operational constraints."
In this article, an analytical solution procedure is described for solving two and three dimensio... more In this article, an analytical solution procedure is described for solving two and three dimensional second order hyperbolic telegraph equation using a reliable semi-analytic method so called the reduced differential transform method (RDTM) subject to the appropriate initial condition. Using this method, it is possible to find exact solution or a closed approximate solution of a differential equation. Various numerical examples are carried out to check the accuracy, efficiency, and convergence of the described method. The method is a powerful mathematical tool for solving a wide range of problems arising in engineering and sciences.
This article discusses the dynamic state analysis of underwater towed-cable when tow-ship changes... more This article discusses the dynamic state analysis of underwater towed-cable when tow-ship changes its speed in a direction making parabolic profile path. A three-dimensional model of underwater towed system is studied. The established governing equations for the system have been solved using the central implicit finite-difference method. The solution of this problem has practical importance in the estimation of dynamic loading and motion, and hence it is directly applicable to the enhancement of safety and the effectiveness of the offshore activities.
AIP, Mar 24, 2014
In this paper, an implicit logarithmic finite difference method (I-LFDM) is implemented for the n... more In this paper, an implicit logarithmic finite difference method (I-LFDM) is implemented for the numerical solution of one dimensional coupled nonlinear Burgers’ equation. The numerical scheme provides a system of nonlinear difference equations which we linearise using Newton's method. The obtained linear system via Newton's method is solved by Gauss elimination with partial pivoting algorithm. To illustrate the accuracy and reliability of the scheme, three numerical examples are described. The obtained numerical solutions are compared well with the exact solutions and those already available.
"In this article, a mathematical model has been developed for the generalized time fractional–ord... more "In this article, a mathematical model has been developed for the generalized time fractional–order biological population model (GTFBPM). The fractional derivative has been described in the Caputo sense. The model has been solved by a recent approximate analytic method so called the fractional reduced differential transform method (FRDTM). Using this method, it is possible to find the exact solution as well as closed approximate solution of a differential equation. Three numerical examples of GTFBPM have been provided in order to check the effectiveness, accuracy and convergence of the method. The special advantage of using this computational technique is that it is very easy to implement and takes small size of computation contrary to other numerical methods while dealing complex and tedious physical problems arising in various branches of natural sciences and engineering.
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A dynamical model of HIV infection of CD4+ T cells is solved numerically using an approximate ana... more A dynamical model of HIV infection of CD4+ T cells is solved numerically using an approximate analytical method so-called the differential transform method (DTM). The solution obtained by the method is an infinite power series for appropriate initial condition, without any discretization, transformation, perturbation, or restrictive conditions. A comparative study between the present method, the classical Euler’s and Runge–Kutta fourth order (RK4) methods is also
carried out.
In this article, an analytical solution based on the series expansion method is proposed to solv... more In this article, an analytical solution based on the series expansion method is proposed to solve the time-fractional telegraph equation (TFTE) in two and three dimensions using a recent and reliable semi-approximate method, namely the reduced differential transform method (RDTM) subjected to the appropriate initial condition. Using RDTM, it is possible to find exact solution or a closed approximate solution of a differential equation. The accuracy, efficiency, and convergence of the method are demonstrated through the four numerical examples.
This article reports two conical shadow models: a spherical Earth conical shadow model (SECSM) an... more This article reports two conical shadow models: a spherical Earth conical shadow model (SECSM) and an oblate Earth conical shadow model (OECSM), and their comparative study to predict umbra and penumbra shadow regions for the low Earth orbiting (LEO) satellites. First model is described using a projection map technique considering the spherical shape of the Earth whereas the second model is illustrated using the line of intersection method for the oblate Earth. Both models have been implemented to four Indian Remote Sensing (IRS) satellites: Oceansat-2, Resourcesat-2, Cartosat-2A and Meghatropics-1. Computed results are compared well with the real time data and the commercial AGI package, Systems Tool Kit (STK).
WASET, Apr 2013
A fully implicit finite-difference method has been proposed for the numerical solutions of one di... more A fully implicit finite-difference method has been proposed for the numerical solutions of one dimensional coupled nonlinear Burgers’ equations on the uniform mesh points. The method forms a system of nonlinear difference equations which is to be solved at each iteration. Newton’s iterative method has been implemented to solve this nonlinear assembled system of equations. The linear system has been solved by Gauss elimination method with partial pivoting algorithm at each iteration of Newton’s method. Three test examples have been carried out to illustrate the accuracy of the method. Computed solutions obtained by proposed scheme have been compared with analytical solutions and those already available in the literature by finding L2 and L∞ errors
The linear analysis of Rayleigh-Taylor instability of the interface between two viscous and diele... more The linear analysis of Rayleigh-Taylor instability of the interface between two viscous and dielectric fluids in the presence of a tangential electric field has been carried out when there is heat and mass transfer across the interface. In our earlier work, the viscous potential flow analysis of Rayleigh-Taylor instability in presence of tangential electric field was studied. Here, we use another irrotational theory in which the discontinuities in the irrotational tangential velocity and shear stress are eliminated in the global energy balance. Stability criterion is given by critical value of applied electric field as well as critical wave number. Various graphs have been drawn to show the effect of various physical parameters such as electric field, heat transfer coefficient, and vapour fraction on the stability of the system. It has been observed that heat transfer and electric field both have stabilizing effect on the stability of the system.
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Papers by Vineet Srivastava
the operational satellites to avoid the collision. This paper describes in-plane orbit maneuvers requirements,
planning and their impact on the spacecraft orbit by considering collision avoidance maneuvers conducted for the six IRS satellites over the last three years. We further emphasis the challenges of scheduling a maneuver to IRS satellites at a very short notice taking into account routine payload operations, on-board and other operational constraints."
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carried out.
the operational satellites to avoid the collision. This paper describes in-plane orbit maneuvers requirements,
planning and their impact on the spacecraft orbit by considering collision avoidance maneuvers conducted for the six IRS satellites over the last three years. We further emphasis the challenges of scheduling a maneuver to IRS satellites at a very short notice taking into account routine payload operations, on-board and other operational constraints."
"
carried out.