Abstract
Paraconsistent mathematics, also called Inconsistent Mathematics, is considered as the study of common mathematical objects, such as sets, numbers and functions, where some contradictions are allowed. Within certain conditions, Paraconsistent logic (PL), which is a non-classical Logic, presents as main property tolerance contradiction in its fundamentals without that the conclusions are invalidated. The PL in its structural form, which uses two annotation values-PAL2v, can be used to substantiate a Differential Calculus with Paraconsistent derivative of first and second order. We introduce here the Paraconsistent Partial Differential Equation (PPDE) aligned with processes of numerical methods for an example application in analysis with Explicit solution of temperature distribution in one-dimensional way. To obtain the results was used an analogy of application of PPDE with the law of heat conduction of Fourier, considering the same mathematical procedures of finite differences.
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