This paper presents a numerical method for solving a nonlinear age-structured population model based on a set of piecewise constant orthogonal functions. The block-pulse functions (BPFs) method is applied to determine the numerical solution of a non-classic type of partial differential equation with an integral boundary condition. BPFs duo to the simple structure can efficiently approximate the solution of systems with local or non-local boundary conditions. Numerical results reveal the accuracy of the proposed method even for the long term simulations.

The modification of the Turia River's course in the 1960s marked a pivotal transformation in Valencia's urban landscape, evolving from a flood protection measure into a hallmark of sustainable urban development. However, recent rainfalls and flooding events produced directly by the phenomenon known as DANA ((Isolated Depression at High Levels) in October 2024 have exposed vulnerabilities in the infrastructure, particularly in the rapidly urbanized southern areas, raising questions about the effectiveness of past solutions in the context of climate change and urban expansion. As a result of this fragility, more than 200 deaths have occurred, along with material losses in 87 municipalities, whose industrial infrastructure accounts for nearly one-third of the economic activity in the Province of Valencia, valued at 479.6 million euros. This paper presents, for the first time, a historical-document-based approach to evaluate the successes and shortcomings of Valencia's flood management strategies through policy and spatial planning analysis. Also, this paper remarks the ongoing challenges and potential strategies for enhancing Valencia's urban resilience, emphasizing the need for innovative water management systems, improved drainage infrastructure, and the renaturalization of flood-prone areas. The lessons learned from Valencia's experience in 1957 and 2024 can inform future urban planning efforts in similar contexts facing the dual pressures of environmental change and urbanization.

Research on community resilience has been ongoing for decades. Several studies have been carried out on resilience in different groups and contexts. However, few address the relationship between community resilience and depopulated rural areas. This study aims to dig deeper into this, considering the concrete impact of population decline in Spain. We carried out a systematic review of the most relevant contributions. A search protocol was developed and used to consult ten databases. Different combinations of terms such as ‘community resilience’, ‘rural’, and ‘depopulation’, or related terms, were used. 22 scientific texts were analysed. We obtained a set of publications that demonstrate the heterogeneity of research methods, approaches and analytical processes applied to the study of this relationship. A mostly qualitative approach was observed, either as the main technique or complementary to documentary reviews. The results underscore the complex nature of rural depopulation and related constructs. It emphasizes the specific importance of community resilience in these territories in terms of social capital, endogenous resources, sustainability, economic dynamism, local responsibility and effective governance. The findings identify a scarce mention to social intervention professions, which should have a more important role due to their core values. In the studies reviewed, it appears as an emerging and scientifically relevant area to explore, both for investigation and intervention purposes. The strength of a multidisciplinary approach to addressing the phenomena appears in the discussion as a main potential line of research.