In this article, a nonlinear fractional Cable equation is solved by a two-grid algorithm combined with finite element (FE) method. A temporal second-order fully discrete two-grid FE scheme, in which the spatial direction is approximated by two-grid FE method and the integer and fractional derivatives in time are discretized by second-order two-step backward difference method and second-order weighted and shifted Grünwald difference (WSGD) scheme, is presented to solve nonlinear fractional Cable equation. The studied algorithm in this paper mainly covers two steps: First, the numerical solution of nonlinear FE scheme on the coarse grid is solved; Second, based on the solution of initial iteration on the coarse grid, the linearized FE system on the fine grid is solved by using Newton iteration. Here, the stability based on fully discrete two-grid method is derived. Moreover, the a priori estimates with second-order convergence rate in time is proved in detail, which is higher than the L1-approximation result with O(τ 2−α + τ 2−β ). Finally, the numerical results by using the two-grid method and FE method are calculated, respectively, and the CPU-time is compared to verify our theoretical results.

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Extensive research on resource-constrained innovation has been conducted by scholars and practitioners in recent years. An interesting research avenue is how firms explore the process of the new product development (NPD) and the ideas generation to foster resource-constrained innovation. However, despite the importance of product development and creative ideas under the resource-constraints contexts, innovation methods for applying to the resource-constrained innovation and designers have received comparatively less attention. As a remedy, this paper proposes a resource-constrained innovation method (RCIM) to generate ideas for the NPD. The RCIM is mainly divided into four sections: Developing the resource-constrained innovation approaches, developing the resource-constrained innovation dimensions, generating the creative ideas and evaluating the creative ideas. First, the resource-constrained innovation algorithms are developed based on success factors, characteristics, and attributes of resource-constrained innovation and the TRIZ (Teopия Peшeния Изoбpeтaтeльcкиx Зaдaч in Russian; Theory of Inventive Problem Solving in English) inventive principles via the systematic literature review (SLR). Second, the innovation dimensions are categorized to structure a target technology by means of the morphological analysis (MA) and the Derwent manual codes (DMCs) mapping based on collected patents. Third, the creative ideas are generated for the NPD by combining the innovation dimensions with the resource-constrained innovation approaches. Finally, the creative ideas are evaluated by the frugal criteria. The RCIM will stimulate designers’ creativity for achieving sustainability and innovation within constraint-based scenarios, MA and TRIZ.

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