Classical Theory of Linear Multistep Methods for Volterra Functional Differential Equations by Yunfei Li, Shoufu Li

“…Based on the linear multistep methods for ordinary differential equations (ODEs) and the canonical interpolation theory that was presented by Shoufu Li who is exactly the second author of this paper, we propose the linear multistep methods for general Volterra functional differential equations (VFDEs) and build the classical stability, consistency, and convergence theories of the methods. …”
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Displacement Field Approximations for Force-Based Elements in Large Displacement Analyses by M. Vahidi, V. Jafari, M. H. Abyaneh, SH. Vahdani

“…The three fields, introduced in this review, are: curvature-based displacement interpolation (CBDI) used in matrix-based flexibility formulations, linear displacement approximation applied in state space, and higher-order displacement approximation utilized again in state space. …”
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On the Bivariate Spectral Homotopy Analysis Method Approach for Solving Nonlinear Evolution Partial Differential Equations by S. S. Motsa

“…The new approach, termed bivariate spectral homotopy analysis method (BISHAM), is based on the use of bivariate Lagrange interpolation in the so-called rule of solution expression of the HAM algorithm. …”
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Implicit One-Step Block Hybrid Third-Derivative Method for the Direct Solution of Initial Value Problems of Second-Order Ordinary Differential Equations by Mohammad Alkasassbeh, Zurni Omar

“…In deriving this method, a power series approximate function is interpolated at {xn,xn+r} while its second and third derivatives are collocated at all points {xn,xn+r,xn+s,xn+t,xn+1} in the given interval. …”
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An Implicit Collocation Method for Direct Solution of Fourth Order Ordinary Differential Equations by B. Alechenu, D.O. Oyewola

“… This paper presented a linear multistep method for solving fourth order initial value problems of ordinary differential equations. Collocation and interpolation methods are adopted in the derivation of the new numerical scheme which is further applied to finding direct solution of fourth order ordinary differentiation equations. …”
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On Generalized Arakawa–Kaneko Zeta Functions with Parameters a,b,c by Nestor G. Acala, Edward Rowe M. Aleluya

“…In this paper, an interpolation formula between these generalized zeta functions and the poly-Bernoulli polynomials with a,b,c parameters is obtained. …”
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Trajectory Planning of Robot based on the Jerk Optimal by Wang Wenjie, Qin Xiansheng, Wang Hongbo, Niu Junlong, Tan Xiaoqun, Zhang Xuefeng

“…The trajectory path is imposed through limits on the waypoints in the Cartesian space,the continuous differentiable cosine curve is used to interpolate the robot trajectory path between the waypoints,and the expected joint angle of robot is calculated by solving the inverse kinematics. …”
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An Implicit Collocation Method for Direct Solution of Fourth Order Ordinary Differential Equations by B. Alechenu, D.O. Oyewola

“… This paper presented a linear multistep method for solving fourth order initial value problems of ordinary differential equations. Collocation and interpolation methods are adopted in the derivation of the new numerical scheme which is further applied to finding direct solution of fourth order ordinary differentiation equations. …”
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Optimization of determination and application of complexly distributed loads on a double curvature cable-stayed covering by V. A. Dagaev, G. M. Purvin, F. S. Shkoliar

“…The use of Grasshopper made it possible to get away from simplification and interpolation of both the magnitude of pressure from snow and wind in several directions and the values of load areas at each point of the cable-stayed network. …”
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Calculation of Correction Factors for Vickers’ Hardness Measurements on a Non-Planar Surface by S. G. Sandomirski, A. L. Val’ko, S. P. Rudenko

“…The K values for d/D ratios not given in the tables are determined by interpolation from the closest to the measured tabulated d/D values. …”
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Repairbads: An automatic and adaptive method to repair bad channels and segments for OPM-MEG by Fulong Wang, Yujie Ma, Tianyu Gao, Yue Tao, Ruonan Wang, Ruochen Zhao, Fuzhi Cao, Yang Gao, Xiaolin Ning

“…Most common methods directly reject or interpolate to repair these bad channels and segments. …”
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Numerical Prediction of Fatigue Life for Landing Gear Considering the Shock Absorber Travel by Haihong Tang, Panglun Liu, Jianbin Ding, Jinsong Cheng, Yiyao Jiang, Bingyan Jiang

“…In this way, the fatigue stress of the MLG with any actual SAT can be obtained by interpolating the stress components of the seven FEMs. …”
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Performance evaluation for JPEG compression on model-based source camera identification by Bo WANG, Jian-feng YIN, Ya-bin LI

“…Focusing on JPEG images transferred by social platform and network media from actual forensic cases,quantities of simulation experiments were carried out to evaluate the performance of three typical methods of model-based source camera identification.The methods are based on the feature of interpolation coefficients of color filter array(CFA),local binary pattern(LBP),and image quality measurement(IQM)with high-order wavelet statis-tic features.The experiments demonstrate that the accuracy decreases rapidly with the compression quality of im-ages decreasing.As a result,methods of model-based source camera identification currently used are demanded bet-ter performance in practical scenes.…”
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Approximate Solutions of Fisher's Type Equations with Variable Coefficients by A. H. Bhrawy, M. A. Alghamdi

“…The spatial derivatives are collocated at a Legendre-Gauss-Lobatto interpolation nodes. The proposed method has the advantage of reducing the problem to a system of ordinary differential equations in time. …”
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Time-optimal Trajectory Planning of 6-DOF Robot based on Genetic Algorithm by He Jianli, Zhu Longying, Cheng Lei, Yin Jiucheng

“…Firstly,by using the seven times B spline curve,the interpolation of the robot position time series is completed. …”
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Phillips-Type q-Bernstein Operators on Triangles by Asif Khan, M. S. Mansoori, Khalid Khan, M. Mursaleen

“…The purpose of the paper is to introduce a new analogue of Phillips-type Bernstein operators Bm,qufu,v and Bn,qvfu,v, their products Pmn,qfu,v and Qnm,qfu,v, their Boolean sums Smn,qfu,v and Tnm,qfu,v on triangle Th, which interpolate a given function on the edges, respectively, at the vertices of triangle using quantum analogue. …”
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Numerical Manifold Method for the Forced Vibration of Thin Plates during Bending by Ding Jun, Chen Song, Wen Wei-Bin, Luo Shao-Ming, Huang Xia

“…A novel numerical manifold method was derived from the cubic B-spline basis function. The new interpolation function is characterized by high-order coordination at the boundary of a manifold element. …”
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Some Properties of Multiple Generalized q-Genocchi Polynomials with Weight and Weak Weight by J. Y. Kang

“…Moreover, we construct a Hurwitz-type zeta function which interpolates multiple generalized q-Genocchi polynomials with weight α and weak weight β and find some combinatorial relations.…”
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Procedure for optimization calculation of structures of suspended electromagnetic separators by G. A. Koschuk, K. I. Nikitin, A. S. Tatevosyan, N. A. Tereshchenko

“…During development of the optimization technique there is used the assumption of the plane-parallel nature of the magnetic field under the pole tips of the electromagnetic separator, thanks to which the formula for magnetic force at the middle of the interpole gap is derived. The effect on the maximum magnetic force of the length of the pole tips, the inter-pole gap and the height of the suspension of the electromagnetic separator has been investigated. …”
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Pullback-Forward Dynamics for Damped Schrödinger Equations with Time-Dependent Forcing by Lianbing She, Yangrong Li, Renhai Wang

“…The method of energy, high-low frequency decomposition, Sobolev embedding, and interpolation are quite involved in calculating a priori pullback or forward bound.…”
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