In this study, we introduce a new numerical technique for solving nonlinear generalized Burgers-Fisher and Burgers-Huxley equations using hybrid B-spline collocation method. This technique is based on usual finite difference scheme and Crank-Nicolson method which are used to discretize the time derivative and spatial derivatives, respectively. Furthermore, hybrid B-spline function is utilized as interpolating functions in spatial dimension. The scheme is verified unconditionally stable using the Von Neumann (Fourier) method. Several test problems are considered to check the accuracy of the proposed scheme. The numerical results are in good agreement with known exact solutions and the existing schemes in literature.

This paper presents a novel approach to numerical solution of a class of fourth-order time fractional partial differential equations (PDEs). The finite difference formulation has been used for temporal discretization, whereas the space discretization is achieved by means of non-polynomial quintic spline method. The proposed algorithm is proved to be stable and convergent. In order to corroborate this work, some test problems have been considered, and the computational outcomes are compared with those found in the exiting literature. It is revealed that the presented scheme is more accurate as compared to current variants on the topic.

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A control chart is very useful to control assignable causes which detect the shifted process parameters (eg, mean and dispersion). Simultaneous monitoring of the process parameters is a well‐known approach utilized for the bilateral processes. In the current study, we proposed the blended control chart that monitors the process mean and process coefficient of variation simultaneously. Further, the sensitivity of control chart is enhanced by incorporating an auxiliary variable. We have utilized the concept of EWMA chart and also the log transformation to transform the distribution of sample coefficient of variation to the normal distribution for structuring a joint monitoring control chart. The performance comparison among proposed control charts is presented. On the basis of ARLs and SDRLs, several advantages of the proposed control charts are diagnosed. The empirical evidence is also provided to support proposed control chart with a real‐life dataset.

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