Papers by RAVIKIRAN MUNDEWADI
International Journal of Mathematics and computational Engineering
In this paper, we study the graph theoretical polynomial known as the Hosoya polynomial obtained ... more In this paper, we study the graph theoretical polynomial known as the Hosoya polynomial obtained from one of the standard classes of graphs called path. Using this polynomial applied for the numerical solution of the nonlinear Fredholm integral equation, which reduces in the algebraic system of equation with collocation points, then solving this system using Newton's iterative with the help of MATLAB, we obtain the required approximate solution. The desired results in terms of a set of continuous polynomials over a closed interval [0, 1]. Illustrative applications show the efficiency, accuracy and validity of the proposed technique.
Journal of Umm Al-Quara University of Applied science, 2024
The numerical solution of Volterra integral equation using one of the graph theoretic polynomial ... more The numerical solution of Volterra integral equation using one of the graph theoretic polynomial is Hosoya polynomial. To reduce the VIEs to a system of algebraic equations by substituting collocation points. To simplify these system by the help of Matlab using Newton's iteration technique, we get the Hosoya coefficients and substitute these coefficients in function approximation to get the required solutions as shown in tables and graphically represent the figures. The error analysis demonstrates the accuracy, stability, and consistency. The proposed method shows efficiency and validity as compared to the existing methods.
International Journal of Mathematics and Computer in Engineering
We present an algorithm for the result of differential equations (DEs) by using linearly independ... more We present an algorithm for the result of differential equations (DEs) by using linearly independent Hosoya polynomials of trees. With the newly adopted strategy, the desired outcome is expanded in the form of a collection of continuous polynomials over an interval. Nevertheless, compared to other methods for solving differential equations, this method’s precision and effectiveness rely on the size of the collection of Hosoya polynomials, and the process is easier. Excellent agreement between the exact and approximate solutions is obtained when the current scheme is used to crack linear and nonlinear equations. Potentially, this method could be used in more intricate systems for which there are no exact solutions.
International Journal of Mathematics and Computer in Engineering
In this study, the Laguerre wavelet-oriented numerical scheme for nonlinear first and second-orde... more In this study, the Laguerre wavelet-oriented numerical scheme for nonlinear first and second-order delay differential equations (DDEs) is offered. The proposed technique is dependent on the truncated series of the Laguerre wavelets approximation of an unknown function. Here, we transform the different ordered DDEs into a system of non-linear algebraic equations with the help of limit points of a sequence of collocation points. Four nonlinear illustrations are involved to prove the efficiency of the planned technique. Obtained results are equated with the current results, indicating the proposed technique’s accuracy and efficiency.
Cosine and Sine (CAS) wavelet collocation method for the numerical solution of Volterra, Fredholm... more Cosine and Sine (CAS) wavelet collocation method for the numerical solution of Volterra, Fredholm integral and integro-differential equations, mixed Volterra-Fredholm integral equations. The method is based Cosine and Sine (CAS) wavelet approximations. The Cosine and Sine (CAS) wavelet is first presented and the resulting Cosine and sine wavelet matrices are utilized to reduce the integral and integro-differential equations into a system of algebraic equations, which is the required Cosine and Sine (CAS) coefficients, are computed using Matlab. The technique is tested on some numerical examples and compared with the exact and existing methods (i.e., Hermite, Legendre and Bernoulli Wavelet). Error analysis is worked out, which shows efficiency of the proposed scheme.
In this paper, we generalized the operational matrix of integration by the clique polynomial of a... more In this paper, we generalized the operational matrix of integration by the clique polynomial of a complete graph. Based on this matrix, the clique polynomial operational matrix method (CPOMM) is proposed for the numerical solution of linear and nonlinear delay differential equations, which is transformed into a system of linear or nonlinear algebraic equations solved effectively with the help of suitable solvers. Illustrative examples are checked through the error analysis for the efficiency of the developed method. The numerical results are comparing splendidly with the corresponding exact solution and existing method.
Graphs obtained by deleting a few edges from the complete graph are referred to as cluster graphs... more Graphs obtained by deleting a few edges from the complete graph are referred to as cluster graphs. We determine expressions for the first and second Zagreb indices, forgotten topological index, and hyper–Zagreb index of four classes of cluster graphs and their complements, as well as expressions for their coindices. In addition, we correct an error of one of the present authors, regrading an expression for the hyper–Zagreb coindex.
In this paper, a Bernoulli wavelet based numerical method for the solution of Fredholm integral e... more In this paper, a Bernoulli wavelet based numerical method for the solution of Fredholm integral equations of the second kind is proposed. The method is based upon Bernoulli wavelet approximations. The Bernoulli wavelet (BW) is first presented and the resulting Bernoulli wavelet matrices are utilized to reduce the Fredholm integral equations into algebraic equations. Solving these equations using MATLAB to obtain Bernoulli coefficients. The numerical results of the proposed method through the illustrative examples is presented in comparison with the exact and existing methods (Haar wavelet method (HWM) [13], Hermite cubic splines (HCS) [11]) of solution from the literature are shown in tables and figures, which show that the validity and applicability of the technique with higher accuracy even for the smaller values of N.
Journal of Information and Optimization Sciences
Haar wavelet collocation method is developed for the numerical solution of nonlinear Fredholm, Vo... more Haar wavelet collocation method is developed for the numerical solution of nonlinear Fredholm, Volterra, mixed VolterraFredholm integral and integro-differential equations. The method is tested on some of illustrative examples and made a comparison with the exact solution and existing methods. It shows that the proposed method yields better results than the others. Hence, the proposed scheme is a new alternative approach and efficient numerical method for the solution of nonlinear integral and integro-differential equations.
Cosine and Sine (CAS) wavelet collocation method for the numerical solution of Volterra, Fredholm... more Cosine and Sine (CAS) wavelet collocation method for the numerical solution of Volterra, Fredholm integral and integro-differential equations, mixed Volterra-Fredholm integral equations. The method is based Cosine and Sine (CAS) wavelet approximations. The Cosine and Sine (CAS) wavelet is first presented and the resulting Cosine and sine wavelet matrices are utilized to reduce the integral and integro-differential equations into a system of algebraic equations, which is the required Cosine and Sine (CAS) coefficients, are computed using Matlab. The technique is tested on some numerical examples and compared with the exact and existing methods (i.e., Hermite, Legendre and Bernoulli Wavelet). Error analysis is worked out, which shows efficiency of the proposed scheme.
The paper presents a novel design for CNC special purpose machine spindle. The design of spindle ... more The paper presents a novel design for CNC special purpose machine spindle. The design of spindle consists of 'system design' and 'mechanical design', where system design takes care of space availability, ergonomics and physical constraints. Models of spindle and the parts of its assembly are made using SOLIDWORKS modeling software tool. The analysis of the spindle shaft and spindle assembly is made for different cutting speeds to know the deflections and stresses in the spindle shaft and spindle assembly parts. Simulation is conducted using ANSYS software tool. The deflections and stresses obtained are found to be within the safe limit. Hence, the present design made is safe for CNC spindle.
The Paper presents Flexible Manufacturing system (FMS) has various tools to outsmart its competit... more The Paper presents Flexible Manufacturing system (FMS) has various tools to outsmart its competitors, achieved through improving productivity through operations, and reduction of delivery time to end users with quality products. VSM is used to reduce Non-value adding practices. Simulated the model of process on arena software. This work helps productivity by improving throughput and by reducing the system unbalance in manufacturing stream after getting the desired output from VSM, comparison is made with the results of Fuzzy logic to know which will be proven better to solve such complicated problems of FMS.
International Journal of Mathematics Trends and Technology
Hermite wavelet collocation method for the numerical solution of Volterra, Fredholm, mixed Volter... more Hermite wavelet collocation method for the numerical solution of Volterra, Fredholm, mixed Volterra-Fredholm integral equations, integro-differential equations and Abel's integral equations. The method is based upon Hermite polynomials and Hermite wavelet approximations. The properties of Hermite wavelet is first presented and the resulting Hermite wavelet matrices are utilized to reduce the integral and integrodifferential equations into system of algebraic equations to get the required Hermite coefficients are computed using Matlab. This technique is tested, some numerical examples and compared with the exact and existing method. Error analysis is worked out, which shows the efficiency of the proposed method.
In this paper, the continues Legendre wavelets constructed on the interval [0,1] are used in solv... more In this paper, the continues Legendre wavelets constructed on the interval [0,1] are used in solving numerical problems involving Fredholm integral equations. This method has been shown to be a powerful numerical tool for finding fast and accurate solutions. We use quadrature formula for the calculation of inner products of any functions, which are required in the approximation for the integral equations. So, Legendre wavelet method required for our subsequent development are given and are utilized to reduce Fredholm integral equation to some algebraic equations. Numerical examples are included to demonstrate the validity and applicability of the technique. Legendre wavelet based numerical solutions are compared with the spline wavelet based solutions [8] and Exact solutions. Legendre wavelet method based solutions are in good agreement with exact one. Finally, the convergence and efficiency of this method is discussed with some illustrative examples, which indicate the ability and accuracy of the Legendre wavelets based numerical method.
In this paper, a Bernoulli wavelet based numerical method for the solution of Fredholm integral e... more In this paper, a Bernoulli wavelet based numerical method for the solution of Fredholm integral equations of the second kind is proposed. The method is based upon Bernoulli wavelet approximations. The Bernoulli wavelet (BW) is first presented and the resulting Bernoulli wavelet matrices are utilized to reduce the Fredholm integral equations into algebraic equations. Solving these equations using MATLAB to obtain Bernoulli coefficients. The numerical results of the proposed method through the illustrative examples is presented in comparison with the exact and existing methods (Haar wavelet method (HWM) [13], Hermite cubic splines (HCS) [11]) of solution from the literature are shown in tables and figures, which show that the validity and applicability of the technique with higher accuracy even for the smaller values of N.
Uploads
Papers by RAVIKIRAN MUNDEWADI