Let TA(f)=integral form n= to 1/2(P_~n(x) + P_b^n(x))dx and let TM(f)=integral form n= to P_((+b)/2)^(n+1)(x)dx, where P_c^n denotes the Taylor polynomial to f at c of order n, where n is even. TA and TM are reach ge...Let TA(f)=integral form n= to 1/2(P_~n(x) + P_b^n(x))dx and let TM(f)=integral form n= to P_((+b)/2)^(n+1)(x)dx, where P_c^n denotes the Taylor polynomial to f at c of order n, where n is even. TA and TM are reach generalizations of the Trapezoidal rule and the midpoint rule, respectively. and are each exact for all polynomial of degree ≤n+1. We let L(f) = αTM(f) + (1-α)TA(f), where α =(2^(n+1)(n+1))/(2^(n+1)(n+1)+1), to obtain a numerical integration rule L which is exact for all polynomials of degree≤n+3 (see Theorem l). The case n = 0 is just the classicol Simpson's rule. We analyze in some detail the case n=2, where our formulae appear to be new. By replacing P_(+b)/2)^(n+1)(x) by the Hermite cabic interpolant at a and b. we obtain some known formulae by a different ap- proach (see [1] and [2]). Finally we discuss some nonlinear numerical integration rules obtained by taking piecewise polynomials of odd degree, each piece being the Taylor polynomial off at a and b. respectively. Of course all of our formulae can be compounded over subintervals of [a, b].展开更多
In this article, we use the Hausdorf distance to treat triple Simpson’s rule of the Henstock triple integral of a fuzzy valued function as well as the error bound of the method. We also introduce δ-fine subdivisions...In this article, we use the Hausdorf distance to treat triple Simpson’s rule of the Henstock triple integral of a fuzzy valued function as well as the error bound of the method. We also introduce δ-fine subdivisions for a Henstock triple integral and numerical example is presented in order to show the application and the consequence of the method.展开更多
This paper presents a novel technique for identifying soil parameters for a wheeled vehicle traversing unknown terrain. The identified soil parameters are required for predicting vehicle drawbar pull and wheel drive t...This paper presents a novel technique for identifying soil parameters for a wheeled vehicle traversing unknown terrain. The identified soil parameters are required for predicting vehicle drawbar pull and wheel drive torque, which in turn can be used for traversability prediction, traction control, and performance optimization of a wheeled vehicle on unknown terrain. The proposed technique is based on the Newton Raphson method. An approximated form of a wheel-soil interaction model based on Composite Simpson's Rule is employed for this purpose. The key soil parameters to be identified are internal friction angle, shear deformation modulus, and lumped pressure-sinkage coefficient. The fourth parameter, cohesion, is not too relevant to vehicle drawbar pull, and is assigned an average value during the identification process. Identified parameters are compared with known values, and shown to be in agreement. The identification method is relatively fast and robust. The identified soil parameters can effectively be used to predict drawbar pull and wheel drive torque with good accuracy. The use of identified soil parameters to design a traversability criterion for wheeled vehicles traversing unknown terrain is presented.展开更多
In order to find stable, accurate, and computationally efficient methods for performing the inverse Laplace transform, a new double transformation approach is proposed. To validate and improve the inversion solution o...In order to find stable, accurate, and computationally efficient methods for performing the inverse Laplace transform, a new double transformation approach is proposed. To validate and improve the inversion solution obtained using the Gaver-Stehfest algorithm, direct Laplace transforms are taken of the numerically inverted transforms to compare with the original function. The numerical direct Laplace transform is implemented with a composite Simpson’s rule. Challenging numerical examples involving periodic and oscillatory functions, are investigated. The numerical examples illustrate the computational accuracy and efficiency of the direct Laplace transform and its inverse due to increasing the precision level and the number of terms included in the expansion. It is found that the number of expansion terms and the precision level selected must be in a harmonious balance in order for correct and stable results to be obtained.展开更多
In this article, we report the derivation of high accuracy finite difference method based on arithmetic average discretization for the solution of Un=F(x,u,u′)+∫K(x,s)ds , 0 x s < 1 subject to natural boundary co...In this article, we report the derivation of high accuracy finite difference method based on arithmetic average discretization for the solution of Un=F(x,u,u′)+∫K(x,s)ds , 0 x s < 1 subject to natural boundary conditions on a non-uniform mesh. The proposed variable mesh approximation is directly applicable to the integro-differential equation with singular coefficients. We need not require any special discretization to obtain the solution near the singular point. The convergence analysis of a difference scheme for the diffusion convection equation is briefly discussed. The presented variable mesh strategy is applicable when the internal grid points of the solution space are both even and odd in number as compared to the method discussed by authors in their previous work in which the internal grid points are strictly odd in number. The advantage of using this new variable mesh strategy is highlighted computationally.展开更多
文摘Let TA(f)=integral form n= to 1/2(P_~n(x) + P_b^n(x))dx and let TM(f)=integral form n= to P_((+b)/2)^(n+1)(x)dx, where P_c^n denotes the Taylor polynomial to f at c of order n, where n is even. TA and TM are reach generalizations of the Trapezoidal rule and the midpoint rule, respectively. and are each exact for all polynomial of degree ≤n+1. We let L(f) = αTM(f) + (1-α)TA(f), where α =(2^(n+1)(n+1))/(2^(n+1)(n+1)+1), to obtain a numerical integration rule L which is exact for all polynomials of degree≤n+3 (see Theorem l). The case n = 0 is just the classicol Simpson's rule. We analyze in some detail the case n=2, where our formulae appear to be new. By replacing P_(+b)/2)^(n+1)(x) by the Hermite cabic interpolant at a and b. we obtain some known formulae by a different ap- proach (see [1] and [2]). Finally we discuss some nonlinear numerical integration rules obtained by taking piecewise polynomials of odd degree, each piece being the Taylor polynomial off at a and b. respectively. Of course all of our formulae can be compounded over subintervals of [a, b].
文摘In this article, we use the Hausdorf distance to treat triple Simpson’s rule of the Henstock triple integral of a fuzzy valued function as well as the error bound of the method. We also introduce δ-fine subdivisions for a Henstock triple integral and numerical example is presented in order to show the application and the consequence of the method.
基金This work was supported in part by the EPSRC (No.GR/S31402/01).
文摘This paper presents a novel technique for identifying soil parameters for a wheeled vehicle traversing unknown terrain. The identified soil parameters are required for predicting vehicle drawbar pull and wheel drive torque, which in turn can be used for traversability prediction, traction control, and performance optimization of a wheeled vehicle on unknown terrain. The proposed technique is based on the Newton Raphson method. An approximated form of a wheel-soil interaction model based on Composite Simpson's Rule is employed for this purpose. The key soil parameters to be identified are internal friction angle, shear deformation modulus, and lumped pressure-sinkage coefficient. The fourth parameter, cohesion, is not too relevant to vehicle drawbar pull, and is assigned an average value during the identification process. Identified parameters are compared with known values, and shown to be in agreement. The identification method is relatively fast and robust. The identified soil parameters can effectively be used to predict drawbar pull and wheel drive torque with good accuracy. The use of identified soil parameters to design a traversability criterion for wheeled vehicles traversing unknown terrain is presented.
文摘In order to find stable, accurate, and computationally efficient methods for performing the inverse Laplace transform, a new double transformation approach is proposed. To validate and improve the inversion solution obtained using the Gaver-Stehfest algorithm, direct Laplace transforms are taken of the numerically inverted transforms to compare with the original function. The numerical direct Laplace transform is implemented with a composite Simpson’s rule. Challenging numerical examples involving periodic and oscillatory functions, are investigated. The numerical examples illustrate the computational accuracy and efficiency of the direct Laplace transform and its inverse due to increasing the precision level and the number of terms included in the expansion. It is found that the number of expansion terms and the precision level selected must be in a harmonious balance in order for correct and stable results to be obtained.
文摘In this article, we report the derivation of high accuracy finite difference method based on arithmetic average discretization for the solution of Un=F(x,u,u′)+∫K(x,s)ds , 0 x s < 1 subject to natural boundary conditions on a non-uniform mesh. The proposed variable mesh approximation is directly applicable to the integro-differential equation with singular coefficients. We need not require any special discretization to obtain the solution near the singular point. The convergence analysis of a difference scheme for the diffusion convection equation is briefly discussed. The presented variable mesh strategy is applicable when the internal grid points of the solution space are both even and odd in number as compared to the method discussed by authors in their previous work in which the internal grid points are strictly odd in number. The advantage of using this new variable mesh strategy is highlighted computationally.