Search results for: fifth order spline interpolation
5225 Cubic Trigonometric B-Spline Applied to Linear Two-Point Boundary Value Problems of Order Two
Authors: Nur Nadiah Abd Hamid , Ahmad Abd. Majid, Ahmad Izani Md. Ismail
Abstract:Linear two-point boundary value problems of order two are solved using cubic trigonometric B-spline interpolation method (CTBIM). Cubic trigonometric B-spline is a piecewise function consisting of trigonometric equations. This method is tested on some problems and the results are compared with cubic B-spline interpolation method (CBIM) from the literature. CTBIM is found to approximate the solution slightly more accurately than CBIM if the problems are trigonometric.
Keywords: trigonometric B-spline, two-point boundary valueproblem, spline interpolation, cubic splineProcedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2386
5224 Extended Cubic B-spline Interpolation Method Applied to Linear Two-Point Boundary Value Problems
Authors: Nur Nadiah Abd Hamid, Ahmad Abd. Majid, Ahmad Izani Md. Ismail
Linear two-point boundary value problem of order two is solved using extended cubic B-spline interpolation method. There is one free parameters, λ, that control the tension of the solution curve. For some λ, this method produced better results than cubic B-spline interpolation method.
Keywords: two-point boundary value problem, B-spline, extendedcubic B-spline.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2043
5223 Solving One-dimensional Hyperbolic Telegraph Equation Using Cubic B-spline Quasi-interpolation
Authors: Marzieh Dosti, Alireza Nazemi
In this paper, the telegraph equation is solved numerically by cubic B-spline quasi-interpolation .We obtain the numerical scheme, by using the derivative of the quasi-interpolation to approximate the spatial derivative of the dependent variable and a low order forward difference to approximate the temporal derivative of the dependent variable. The advantage of the resulting scheme is that the algorithm is very simple so it is very easy to implement. The results of numerical experiments are presented, and are compared with analytical solutions by calculating errors L2 and L∞ norms to confirm the good accuracy of the presented scheme.
Keywords: Cubic B-spline, quasi-interpolation, collocation method, second-order hyperbolic telegraph equation.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2653
5222 Overview of Adaptive Spline Interpolation
Authors: Rongli Gai, Zhiyuan Chang, Xiaohong Wang, Jingyu Liu
In view of various situations in the interpolation process, most researchers use self-adaptation to adjust the interpolation process, which is also one of the current and future research hotspots in the field of CNC (Computerized Numerical Control) machining. In the interpolation process, according to the overview of the spline curve interpolation algorithm, the adaptive analysis is carried out from the factors affecting the interpolation process. The adaptive operation is reflected in various aspects, such as speed, parameters, errors, nodes, feed rates, random period, sensitive point, step size, curvature, adaptive segmentation, adaptive optimization, etc. This paper will analyze and summarize the research of adaptive imputation in the direction of the above factors affecting imputation.
Keywords: Adaptive algorithm, CNC machining, interpolation constraints, spline curve interpolation.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 119
5221 A New Quadrature Rule Derived from Spline Interpolation with Error Analysis
Authors: Hadi Taghvafard
Abstract:We present a new quadrature rule based on the spline interpolation along with the error analysis. Moreover, some error estimates for the reminder when the integrand is either a Lipschitzian function, a function of bounded variation or a function whose derivative belongs to Lp are given. We also give some examples to show that, practically, the spline rule is better than the trapezoidal rule.
Keywords: Quadrature, Spline interpolation, Trapezoidal rule, Numericalintegration, Error analysis.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2088
5220 Line Heating Forming: Methodology and Application Using Kriging and Fifth Order Spline Formulations
Authors: Henri Champliaud, Zhengkun Feng, Ngan Van Lê, Javad Gholipour
Abstract:In this article, a method is presented to effectively estimate the deformed shape of a thick plate due to line heating. The method uses a fifth order spline interpolation, with up to C3 continuity at specific points to compute the shape of the deformed geometry. First and second order derivatives over a surface are the resulting parameters of a given heating line on a plate. These parameters are determined through experiments and/or finite element simulations. Very accurate kriging models are fitted to real or virtual surfaces to build-up a database of maps. Maps of first and second order derivatives are then applied on numerical plate models to evaluate their evolving shapes through a sequence of heating lines. Adding an optimization process to this approach would allow determining the trajectories of heating lines needed to shape complex geometries, such as Francis turbine blades.
Keywords: Deformation, kriging, fifth order spline interpolation, first, second and third order derivatives, C3 continuity, line heating, plate forming, thermal forming.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1948
5219 Evaluating Sinusoidal Functions by a Low Complexity Cubic Spline Interpolator with Error Optimization
Authors: Abhijit Mitra, Harpreet Singh Dhillon
We present a novel scheme to evaluate sinusoidal functions with low complexity and high precision using cubic spline interpolation. To this end, two different approaches are proposed to find the interpolating polynomial of sin(x) within the range [- π , π]. The first one deals with only a single data point while the other with two to keep the realization cost as low as possible. An approximation error optimization technique for cubic spline interpolation is introduced next and is shown to increase the interpolator accuracy without increasing complexity of the associated hardware. The architectures for the proposed approaches are also developed, which exhibit flexibility of implementation with low power requirement.
Keywords: Arithmetic, spline interpolator, hardware design, erroranalysis, optimization methods.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1922
5218 A Review on Higher Order Spline Techniques for Solving Burgers Equation Using B-Spline Methods and Variation of B-Spline Techniques
Authors: Maryam Khazaei Pool, Lori Lewis
This is a summary of articles based on higher order B-splines methods and the variation of B-spline methods such as Quadratic B-spline Finite Elements Method, Exponential Cubic B-Spline Method Septic B-spline Technique, Quintic B-spline Galerkin Method, and B-spline Galerkin Method based on the Quadratic B-spline Galerkin method (QBGM) and Cubic B-spline Galerkin method (CBGM). In this paper we study the B-spline methods and variations of B-spline techniques to find a numerical solution to the Burgers’ equation. A set of fundamental definitions including Burgers equation, spline functions, and B-spline functions are provided. For each method, the main technique is discussed as well as the discretization and stability analysis. A summary of the numerical results is provided and the efficiency of each method presented is discussed. A general conclusion is provided where we look at a comparison between the computational results of all the presented schemes. We describe the effectiveness and advantages of these methods.
Keywords: Burgers’ Equation, Septic B-spline, Modified Cubic B-Spline Differential Quadrature Method, Exponential Cubic B-Spline Technique, B-Spline Galerkin Method, and Quintic B-Spline Galerkin Method.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 28
5217 Visualization of Sediment Thickness Variation for Sea Bed Logging using Spline Interpolation
Authors: Hanita Daud, Noorhana Yahya, Vijanth Sagayan, Muizuddin Talib
Abstract:This paper discusses on the use of Spline Interpolation and Mean Square Error (MSE) as tools to process data acquired from the developed simulator that shall replicate sea bed logging environment. Sea bed logging (SBL) is a new technique that uses marine controlled source electromagnetic (CSEM) sounding technique and is proven to be very successful in detecting and characterizing hydrocarbon reservoirs in deep water area by using resistivity contrasts. It uses very low frequency of 0.1Hz to 10 Hz to obtain greater wavelength. In this work the in house built simulator was used and was provided with predefined parameters and the transmitted frequency was varied for sediment thickness of 1000m to 4000m for environment with and without hydrocarbon. From series of simulations, synthetics data were generated. These data were interpolated using Spline interpolation technique (degree of three) and mean square error (MSE) were calculated between original data and interpolated data. Comparisons were made by studying the trends and relationship between frequency and sediment thickness based on the MSE calculated. It was found that the MSE was on increasing trends in the set up that has the presence of hydrocarbon in the setting than the one without. The MSE was also on decreasing trends as sediment thickness was increased and with higher transmitted frequency.
Keywords: Spline Interpolation, Mean Square Error, Sea Bed Logging, Controlled Source ElectromagneticProcedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1532
5216 Application of Higher Order Splines for Boundary Value Problems
Authors: Pankaj Kumar Srivastava
Abstract:Bringing forth a survey on recent higher order spline techniques for solving boundary value problems in ordinary differential equations. Here we have discussed the summary of the articles since 2000 till date based on higher order splines like Septic, Octic, Nonic, Tenth, Eleventh, Twelfth and Thirteenth Degree splines. Comparisons of methods with own critical comments as remarks have been included.
Keywords: Septic spline, Octic spline, Nonic spline, Tenth, Eleventh, Twelfth and Thirteenth Degree spline, parametric and non-parametric splines, thermal instability, astrophysics.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2604
5215 Quartic Nonpolynomial Spline Solutions for Third Order Two-Point Boundary Value Problem
Authors: Talaat S. El-Danaf
Abstract:In this paper, we develop quartic nonpolynomial spline method for the numerical solution of third order two point boundary value problems. It is shown that the new method gives approximations, which are better than those produced by other spline methods. Convergence analysis of the method is discussed through standard procedures. Two numerical examples are given to illustrate the applicability and efficiency of the novel method.
Keywords: Quartic nonpolynomial spline, Two-point boundary value problem.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1892
5214 Numerical Grid Generation of Oceanic Model for the Andaman Sea
Authors: Nitima Aschariyaphotha, Pratan Sakkaplangkul, Anirut Luadsong
Abstract:The study of the Andaman Sea can be studied by using the oceanic model; therefore the grid covering the study area should be generated. This research aims to generate grid covering the Andaman Sea, situated between longitudes 90◦E to 101◦E and latitudes 1◦N to 18◦N. A horizontal grid is an orthogonal curvilinear with 87 × 217 grid points. The methods used in this study are cubic spline and bilinear interpolations. The boundary grid points are generated by spline interpolation while the interior grid points have to be specified by bilinear interpolation method. A vertical grid is sigma coordinate with 15 layers of water column.
Keywords: Sigma Coordinate, Curvilinear Coordinate, AndamanSea.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1457
5213 Quintic Spline Solution of Fourth-Order Parabolic Equations Arising in Beam Theory
Authors: Reza Mohammadi, Mahdieh Sahebi
Abstract:We develop a method based on polynomial quintic spline for numerical solution of fourth-order non-homogeneous parabolic partial differential equation with variable coefficient. By using polynomial quintic spline in off-step points in space and finite difference in time directions, we obtained two three level implicit methods. Stability analysis of the presented method has been carried out. We solve four test problems numerically to validate the derived method. Numerical comparison with other methods shows the superiority of presented scheme.
Keywords: Fourth-order parabolic equation, variable coefficient, polynomial quintic spline, off-step points, stability analysis.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1065
5212 Statistical Approach to Basis Function Truncation in Digital Interpolation Filters
Authors: F. Castillo, J. Arellano, S. Sánchez
Abstract:In this paper an alternative analysis in the time domain is described and the results of the interpolation process are presented by means of functions that are based on the rule of conditional mathematical expectation and the covariance function. A comparison between the interpolation error caused by low order filters and the classic sinc(t) truncated function is also presented. When fewer samples are used, low-order filters have less error. If the number of samples increases, the sinc(t) type functions are a better alternative. Generally speaking there is an optimal filter for each input signal which depends on the filter length and covariance function of the signal. A novel scheme of work for adaptive interpolation filters is also presented.
Keywords: Interpolation, basis function, over-sampling.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1356
5211 Non-Polynomial Spline Solution of Fourth-Order Obstacle Boundary-Value Problems
Authors: Jalil Rashidinia, Reza Jalilian
Abstract:In this paper we use quintic non-polynomial spline functions to develop numerical methods for approximation to the solution of a system of fourth-order boundaryvalue problems associated with obstacle, unilateral and contact problems. The convergence analysis of the methods has been discussed and shown that the given approximations are better than collocation and finite difference methods. Numerical examples are presented to illustrate the applications of these methods, and to compare the computed results with other known methods.
Keywords: Quintic non-polynomial spline, Boundary formula, Convergence, Obstacle problems.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1687
5210 A General Segmentation Scheme for Contouring Kidney Region in Ultrasound Kidney Images using Improved Higher Order Spline Interpolation
Authors: K. Bommanna Raja, M.Madheswaran, K.Thyagarajah
Abstract:A higher order spline interpolated contour obtained with up-sampling of homogenously distributed coordinates for segmentation of kidney region in different classes of ultrasound kidney images has been developed and presented in this paper. The performance of the proposed method is measured and compared with modified snake model contour, Markov random field contour and expert outlined contour. The validation of the method is made in correspondence with expert outlined contour using maximum coordinate distance, Hausdorff distance and mean radial distance metrics. The results obtained reveal that proposed scheme provides optimum contour that agrees well with expert outlined contour. Moreover this technique helps to preserve the pixels-of-interest which in specific defines the functional characteristic of kidney. This explores various possibilities in implementing computer-aided diagnosis system exclusively for US kidney images.
Keywords: Ultrasound Kidney Image – Kidney Segmentation –Active Contour – Markov Random Field – Higher Order SplineInterpolationProcedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1648
5209 Feature Preserving Image Interpolation and Enhancement Using Adaptive Bidirectional Flow
Authors: Shujun Fu, Qiuqi Ruan, Wenqia Wang
Image interpolation is a common problem in imaging applications. However, most interpolation algorithms in existence suffer visually to some extent the effects of blurred edges and jagged artifacts in the image. This paper presents an adaptive feature preserving bidirectional flow process, where an inverse diffusion is performed to enhance edges along the normal directions to the isophote lines (edges), while a normal diffusion is done to remove artifacts (''jaggies'') along the tangent directions. In order to preserve image features such as edges, angles and textures, the nonlinear diffusion coefficients are locally adjusted according to the first and second order directional derivatives of the image. Experimental results on synthetic images and nature images demonstrate that our interpolation algorithm substantially improves the subjective quality of the interpolated images over conventional interpolations.
Keywords: anisotropic diffusion, bidirectional flow, directionalderivatives, edge enhancement, image interpolation, inverse flow, shock filter.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1388
5208 Beta-spline Surface Fitting to Multi-slice Images
Authors: Normi Abdul Hadi, Arsmah Ibrahim, Fatimah Yahya, Jamaludin Md. Ali
Abstract:Beta-spline is built on G2 continuity which guarantees smoothness of generated curves and surfaces using it. This curve is preferred to be used in object design rather than reconstruction. This study however, employs the Beta-spline in reconstructing a 3- dimensional G2 image of the Stanford Rabbit. The original data consists of multi-slice binary images of the rabbit. The result is then compared with related works using other techniques.
Keywords: Beta-spline, multi-slice image, rectangular surface, 3D reconstructionProcedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1770
5207 Cantor Interpolating Spline to Design Electronic Mail Boxes
Authors: Adil Al-Rammahi
Electronic mail is very important in present time. Many researchers work for designing, improving, securing, fasting, goodness and others fields in electronic mail. This paper introduced new algorithm to use Cantor sets and cubic spline interpolating function in the electronic mail design. Cantor sets used as the area (or domain) of the mail, while spline function used for designing formula. The roots of spline function versus Cantor sets used as the controller admin. The roots calculated by the numerical Newton – Raphson's method. The result of this algorithm was promised.
Keywords: Cantor sets, spline, electronic mail design, Newton – Raphson's method.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1482
5206 A Comparison of the Nonparametric Regression Models using Smoothing Spline and Kernel Regression
Authors: Dursun Aydin
Abstract:This paper study about using of nonparametric models for Gross National Product data in Turkey and Stanford heart transplant data. It is discussed two nonparametric techniques called smoothing spline and kernel regression. The main goal is to compare the techniques used for prediction of the nonparametric regression models. According to the results of numerical studies, it is concluded that smoothing spline regression estimators are better than those of the kernel regression.
Keywords: Kernel regression, Nonparametric models, Prediction, Smoothing spline.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2961
5205 Numerical Solution for Integro-Differential Equations by Using Quartic B-Spline Wavelet and Operational Matrices
Authors: Khosrow Maleknejad, Yaser Rostami
In this paper, Semi-orthogonal B-spline scaling functions and wavelets and their dual functions are presented to approximate the solutions of integro-differential equations.The B-spline scaling functions and wavelets, their properties and the operational matrices of derivative for this function are presented to reduce the solution of integro-differential equations to the solution of algebraic equations. Here we compute B-spline scaling functions of degree 4 and their dual, then we will show that by using them we have better approximation results for the solution of integro-differential equations in comparison with less degrees of scaling functions
Keywords: Integro-differential equations, Quartic B-spline wavelet, Operational matrices.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3000
5204 Design of Compliant Mechanism Based Microgripper with Three Finger Using Topology Optimization
Authors: R. Bharanidaran, B. T. Ramesh
High precision in motion is required to manipulate the micro objects in precision industries for micro assembly, cell manipulation etc. Precision manipulation is achieved based on the appropriate mechanism design of micro devices such as microgrippers. Design of a compliant based mechanism is the better option to achieve a highly precised and controlled motion. This research article highlights the method of designing a compliant based three fingered microgripper suitable for holding asymmetric objects. Topological optimization technique, a systematic method is implemented in this research work to arrive a topologically optimized design of the mechanism needed to perform the required micro motion of the gripper. Optimization technique has a drawback of generating senseless regions such as node to node connectivity and staircase effect at the boundaries. Hence, it is required to have post processing of the design to make it manufacturable. To reduce the effect of post processing stage and to preserve the edges of the image, a cubic spline interpolation technique is introduced in the MATLAB program. Structural performance of the topologically developed mechanism design is tested using finite element method (FEM) software. Further the microgripper structure is examined to find its fatigue life and vibration characteristics.
Keywords: Compliant mechanism, Cubic spline interpolation, FEM, Topology optimization.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3448
5203 Design of Nonlinear Observer by Using Chebyshev Interpolation based on Formal Linearization
Authors: Kazuo Komatsu, Hitoshi Takata
Abstract:This paper discusses a design of nonlinear observer by a formal linearization method using an application of Chebyshev Interpolation in order to facilitate processes for synthesizing a nonlinear observer and to improve the precision of linearization. A dynamic nonlinear system is linearized with respect to a linearization function, and a measurement equation is transformed into an augmented linear one by the formal linearization method which is based on Chebyshev interpolation. To the linearized system, a linear estimation theory is applied and a nonlinear observer is derived. To show effectiveness of the observer design, numerical experiments are illustrated and they indicate that the design shows remarkable performances for nonlinear systems.
Keywords: nonlinear system, nonlinear observer, formal linearization, Chebyshev interpolation.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1458
5202 Interpolation of Geofield Parameters
Authors: A. Pashayev, C. Ardil, R. Sadiqov
Various methods of geofield parameters restoration (by algebraic polynoms; filters; rational fractions; interpolation splines; geostatistical methods – kriging; search methods of nearest points – inverse distance, minimum curvature, local – polynomial interpolation; neural networks) have been analyzed and some possible mistakes arising during geofield surface modeling have been presented.
Keywords: interpolation methods, geofield parameters, neural networks.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1587
5201 Adaptive Bidirectional Flow for Image Interpolation and Enhancement
Authors: Shujun Fu, Qiuqi Ruan, Wenqia Wang
Image interpolation is a common problem in imaging applications. However, most interpolation algorithms in existence suffer visually the effects of blurred edges and jagged artifacts in the image to some extent. This paper presents an adaptive feature preserving bidirectional flow process, where an inverse diffusion is performed to sharpen edges along the normal directions to the isophote lines (edges), while a normal diffusion is done to remove artifacts (“jaggies") along the tangent directions. In order to preserve image features such as edges, corners and textures, the nonlinear diffusion coefficients are locally adjusted according to the directional derivatives of the image. Experimental results on synthetic images and nature images demonstrate that our interpolation algorithm substantially improves the subjective quality of the interpolated images over conventional interpolations.
Keywords: anisotropic diffusion, bidirectional flow, directional derivatives, edge enhancement, image interpolation, inverse flow, shock filter.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1420
5200 Application of Generalized NAUT B-Spline Curveon Circular Domain to Generate Circle Involute
Authors: Ashok Ganguly, Pranjali Arondekar
In the present paper, we use generalized B-Spline curve in trigonometric form on circular domain, to capture the transcendental nature of circle involute curve and uncertainty characteristic of design. The required involute curve get generated within the given tolerance limit and is useful in gear design.
Keywords: Bézier, Circle Involute, NAUT B-Spline, Spur Gear.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1682
5199 Non-Polynomial Spline Method for the Solution of Problems in Calculus of Variations
Authors: M. Zarebnia, M. Hoshyar, M. Sedaghati
Abstract:In this paper, a numerical solution based on nonpolynomial cubic spline functions is used for finding the solution of boundary value problems which arise from the problems of calculus of variations. This approximation reduce the problems to an explicit system of algebraic equations. Some numerical examples are also given to illustrate the accuracy and applicability of the presented method.
Keywords: Calculus of variation; Non-polynomial spline functions; Numerical methodProcedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1841
5198 GMDH Modeling Based on Polynomial Spline Estimation and Its Applications
Authors: LI qiu-min, TIAN yi-xiang, ZHANG gao-xun
GMDH algorithm can well describe the internal structure of objects. In the process of modeling, automatic screening of model structure and variables ensure the convergence rate.This paper studied a new GMDH model based on polynomial spline stimation. The polynomial spline function was used to instead of the transfer function of GMDH to characterize the relationship between the input variables and output variables. It has proved that the algorithm has the optimal convergence rate under some conditions. The empirical results show that the algorithm can well forecast Consumer Price Index (CPI).
Keywords: spline, GMDH, nonparametric, bias, forecast.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1985
5197 Constant Order Predictor Corrector Method for the Solution of Modeled Problems of First Order IVPs of ODEs
Authors: A. A. James, A. O. Adesanya, M. R. Odekunle, D. G. Yakubu
This paper examines the development of one step, five hybrid point method for the solution of first order initial value problems. We adopted the method of collocation and interpolation of power series approximate solution to generate a continuous linear multistep method. The continuous linear multistep method was evaluated at selected grid points to give the discrete linear multistep method. The method was implemented using a constant order predictor of order seven over an overlapping interval. The basic properties of the derived corrector was investigated and found to be zero stable, consistent and convergent. The region of absolute stability was also investigated. The method was tested on some numerical experiments and found to compete favorably with the existing methods.
Keywords: Interpolation, Approximate Solution, Collocation, Differential system, Half step, Converges, Block method, Efficiency.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2198
5196 Spline Collocation for Solving System of Fredholm and Volterra Integral Equations
Authors: N. Ebrahimi, J. Rashidinia
In this paper, numerical solution of system of Fredholm and Volterra integral equations by means of the Spline collocation method is considered. This approximation reduces the system of integral equations to an explicit system of algebraic equations. The solution is collocated by cubic B-spline and the integrand is approximated by the Newton-Cotes formula. The error analysis of proposed numerical method is studied theoretically. The results are compared with the results obtained by other methods to illustrate the accuracy and the implementation of our method.
Keywords: Convergence analysis, Cubic B-spline, Newton- Cotes formula, System of Fredholm and Volterra integral equations.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2051